[{"status":"public","abstract":[{"text":"Abstract\r\n In a smoothly bounded convex domain \r\n \r\n \r\n Ω\r\n ⊂\r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n \r\n${\\Omega}\\subset {\\mathbb{R}}^{n}$\r\n\r\n \r\n \r\n with n ≥ 1, a no-flux initial-boundary value problem for\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n \r\n \r\n t\r\n \r\n \r\n =\r\n Δ\r\n \r\n \r\n u\r\n ϕ\r\n \r\n (\r\n \r\n v\r\n \r\n )\r\n \r\n \r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n v\r\n \r\n \r\n t\r\n \r\n \r\n =\r\n Δ\r\n v\r\n −\r\n u\r\n v\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n$$\\begin{cases}_{t}={\\Delta}\\left(u\\phi \\left(v\\right)\\right),\\quad \\hfill \\\\ {v}_{t}={\\Delta}v-uv,\\quad \\hfill \\end{cases}$$\r\n\r\n \r\n \r\n is considered under the assumption that near the origin, the function ϕ suitably generalizes the prototype given by\r\n \r\n \r\n ϕ\r\n \r\n (\r\n \r\n ξ\r\n \r\n )\r\n \r\n =\r\n \r\n \r\n ξ\r\n \r\n \r\n α\r\n \r\n \r\n ,\r\n \r\n ξ\r\n ∈\r\n \r\n [\r\n \r\n 0\r\n ,\r\n \r\n \r\n ξ\r\n \r\n \r\n 0\r\n \r\n \r\n \r\n ]\r\n \r\n .\r\n \r\n \r\n$$\\phi \\left(\\xi \\right)={\\xi }^{\\alpha },\\qquad \\xi \\in \\left[0,{\\xi }_{0}\\right].$$\r\n\r\n \r\n \r\n By means of separate approaches, it is shown that in both cases α ∈ (0, 1) and α ∈ [1, 2] some global weak solutions exist which, inter alia, satisfy\r\n \r\n \r\n C\r\n \r\n (\r\n \r\n T\r\n \r\n )\r\n \r\n ≔\r\n \r\n \r\n ess sup\r\n \r\n \r\n t\r\n ∈\r\n \r\n (\r\n \r\n 0\r\n ,\r\n T\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n \r\n \r\n Ω\r\n \r\n \r\n u\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n ln\r\n ⁡\r\n u\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n <\r\n ∞\r\n \r\n for all \r\n T\r\n >\r\n 0\r\n ,\r\n \r\n \r\n$$C\\left(T\\right){:=}\\underset{t\\in \\left(0,T\\right)}{\\text{ess\\,sup}}{\\int }_{{\\Omega}}u\\left(\\cdot ,t\\right)\\mathrm{ln}u\\left(\\cdot ,t\\right){< }\\infty \\qquad \\text{for\\,all\\,}T{ >}0,$$\r\n\r\n \r\n \r\n with sup\r\n T>0\r\n C(T) < ∞ if α ∈ [1, 2].","lang":"eng"}],"type":"journal_article","publication":"Advanced Nonlinear Studies","language":[{"iso":"eng"}],"user_id":"31496","_id":"63264","citation":{"ama":"Winkler M. A degenerate migration-consumption model in domains of arbitrary dimension. Advanced Nonlinear Studies. 2024;24(3):592-615. doi:10.1515/ans-2023-0131","ieee":"M. Winkler, “A degenerate migration-consumption model in domains of arbitrary dimension,” Advanced Nonlinear Studies, vol. 24, no. 3, pp. 592–615, 2024, doi: 10.1515/ans-2023-0131.","chicago":"Winkler, Michael. “A Degenerate Migration-Consumption Model in Domains of Arbitrary Dimension.” Advanced Nonlinear Studies 24, no. 3 (2024): 592–615. https://doi.org/10.1515/ans-2023-0131.","mla":"Winkler, Michael. “A Degenerate Migration-Consumption Model in Domains of Arbitrary Dimension.” Advanced Nonlinear Studies, vol. 24, no. 3, Walter de Gruyter GmbH, 2024, pp. 592–615, doi:10.1515/ans-2023-0131.","short":"M. Winkler, Advanced Nonlinear Studies 24 (2024) 592–615.","bibtex":"@article{Winkler_2024, title={A degenerate migration-consumption model in domains of arbitrary dimension}, volume={24}, DOI={10.1515/ans-2023-0131}, number={3}, journal={Advanced Nonlinear Studies}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2024}, pages={592–615} }","apa":"Winkler, M. (2024). A degenerate migration-consumption model in domains of arbitrary dimension. Advanced Nonlinear Studies, 24(3), 592–615. https://doi.org/10.1515/ans-2023-0131"},"intvolume":" 24","page":"592-615","year":"2024","issue":"3","publication_status":"published","publication_identifier":{"issn":["2169-0375"]},"doi":"10.1515/ans-2023-0131","title":"A degenerate migration-consumption model in domains of arbitrary dimension","date_created":"2025-12-18T19:09:41Z","author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"volume":24,"publisher":"Walter de Gruyter GmbH","date_updated":"2025-12-18T20:10:00Z"},{"publication_status":"published","publication_identifier":{"issn":["0025-5831","1432-1807"]},"issue":"2","year":"2024","citation":{"chicago":"Winkler, Michael. “Externally Forced Blow-up and Optimal Spaces for Source Regularity in the Two-Dimensional Navier–Stokes System.” Mathematische Annalen 391, no. 2 (2024): 3023–54. https://doi.org/10.1007/s00208-024-02987-6.","ieee":"M. Winkler, “Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system,” Mathematische Annalen, vol. 391, no. 2, pp. 3023–3054, 2024, doi: 10.1007/s00208-024-02987-6.","ama":"Winkler M. Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system. Mathematische Annalen. 2024;391(2):3023-3054. doi:10.1007/s00208-024-02987-6","mla":"Winkler, Michael. “Externally Forced Blow-up and Optimal Spaces for Source Regularity in the Two-Dimensional Navier–Stokes System.” Mathematische Annalen, vol. 391, no. 2, Springer Science and Business Media LLC, 2024, pp. 3023–54, doi:10.1007/s00208-024-02987-6.","short":"M. Winkler, Mathematische Annalen 391 (2024) 3023–3054.","bibtex":"@article{Winkler_2024, title={Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system}, volume={391}, DOI={10.1007/s00208-024-02987-6}, number={2}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2024}, pages={3023–3054} }","apa":"Winkler, M. (2024). Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system. Mathematische Annalen, 391(2), 3023–3054. https://doi.org/10.1007/s00208-024-02987-6"},"page":"3023-3054","intvolume":" 391","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:13:05Z","date_created":"2025-12-18T19:02:09Z","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"volume":391,"title":"Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system","doi":"10.1007/s00208-024-02987-6","type":"journal_article","publication":"Mathematische Annalen","abstract":[{"text":"Abstract\r\n The Navier–Stokes system \r\n \r\n $$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t + (u\\cdot \\nabla ) u =\\Delta u+\\nabla P + f(x,t), \\\\ \\nabla \\cdot u=0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n +\r\n \r\n (\r\n u\r\n ·\r\n ∇\r\n )\r\n \r\n u\r\n =\r\n Δ\r\n u\r\n +\r\n ∇\r\n P\r\n +\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ∇\r\n ·\r\n u\r\n =\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered along with homogeneous Dirichlet boundary conditions in a smoothly bounded planar domain \r\n \r\n $$\\Omega $$\r\n \r\n Ω\r\n \r\n \r\n . It is firstly, inter alia, observed that if \r\n \r\n $$T>0$$\r\n \r\n \r\n T\r\n >\r\n 0\r\n \r\n \r\n \r\n and \r\n \r\n $$\\begin{aligned} \\int _0^T \\bigg \\{ \\int _\\Omega |f(x,t)| \\cdot \\ln ^\\frac{1}{2} \\big (|f(x,t)|+1\\big ) dx \\bigg \\}^2 dt <\\infty , \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n 0\r\n T\r\n \r\n \r\n {\r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n |\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n ·\r\n \r\n ln\r\n \r\n 1\r\n 2\r\n \r\n \r\n \r\n (\r\n \r\n \r\n |\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n +\r\n 1\r\n \r\n )\r\n \r\n d\r\n x\r\n \r\n \r\n }\r\n \r\n 2\r\n \r\n d\r\n t\r\n <\r\n ∞\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n then for all divergence-free \r\n \r\n $$u_0\\in L^2(\\Omega ;{\\mathbb {R}}^2)$$\r\n \r\n \r\n \r\n u\r\n 0\r\n \r\n ∈\r\n \r\n L\r\n 2\r\n \r\n \r\n (\r\n Ω\r\n ;\r\n \r\n \r\n R\r\n \r\n 2\r\n \r\n )\r\n \r\n \r\n \r\n \r\n , a corresponding initial-boundary value problem admits a weak solution u with \r\n \r\n $$u|_{t=0}=u_0$$\r\n \r\n \r\n \r\n \r\n u\r\n |\r\n \r\n \r\n t\r\n =\r\n 0\r\n \r\n \r\n =\r\n \r\n u\r\n 0\r\n \r\n \r\n \r\n \r\n . For any positive and nondecreasing \r\n \r\n $$L\\in C^0([0,\\infty ))$$\r\n \r\n \r\n L\r\n ∈\r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n such that \r\n \r\n $$\\begin{aligned} \\frac{L(\\xi )}{\\ln ^\\frac{1}{2} \\xi } \\rightarrow 0 \\qquad \\text{ as } \\xi \\rightarrow \\infty , \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n L\r\n (\r\n ξ\r\n )\r\n \r\n \r\n \r\n ln\r\n \r\n 1\r\n 2\r\n \r\n \r\n ξ\r\n \r\n \r\n →\r\n 0\r\n \r\n \r\n as\r\n \r\n ξ\r\n →\r\n ∞\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n this is complemented by a statement on nonexistence of such a solution in the presence of smooth initial data and a suitably constructed \r\n \r\n $$f:\\Omega \\times (0,T)\\rightarrow {\\mathbb {R}}^2$$\r\n \r\n \r\n f\r\n :\r\n Ω\r\n ×\r\n \r\n (\r\n 0\r\n ,\r\n T\r\n )\r\n \r\n →\r\n \r\n \r\n R\r\n \r\n 2\r\n \r\n \r\n \r\n \r\n fulfilling \r\n \r\n $$\\begin{aligned} \\int _0^T \\bigg \\{ \\int _\\Omega |f(x,t)| \\cdot L\\big (|f(x,t)|\\big ) dx \\bigg \\}^2 dt < \\infty . \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n 0\r\n T\r\n \r\n \r\n {\r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n |\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n ·\r\n \r\n L\r\n \r\n (\r\n \r\n |\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n )\r\n \r\n d\r\n x\r\n \r\n \r\n \r\n }\r\n \r\n 2\r\n \r\n d\r\n t\r\n <\r\n ∞\r\n .\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n This resolves a fine structure in the borderline case \r\n \r\n $$p=1$$\r\n \r\n \r\n p\r\n =\r\n 1\r\n \r\n \r\n \r\n and \r\n \r\n $$q=2$$\r\n \r\n \r\n q\r\n =\r\n 2\r\n \r\n \r\n \r\n appearing in results on existence of weak solutions for sources in \r\n \r\n $$L^q((0,T);L^p(\\Omega ;{\\mathbb {R}}^2))$$\r\n \r\n \r\n \r\n L\r\n q\r\n \r\n \r\n (\r\n \r\n (\r\n 0\r\n ,\r\n T\r\n )\r\n \r\n ;\r\n \r\n L\r\n p\r\n \r\n \r\n (\r\n Ω\r\n ;\r\n \r\n \r\n R\r\n \r\n 2\r\n \r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n when \r\n \r\n $$p\\in (1,\\infty ]$$\r\n \r\n \r\n p\r\n ∈\r\n (\r\n 1\r\n ,\r\n ∞\r\n ]\r\n \r\n \r\n \r\n and \r\n \r\n $$q\\in [1,\\infty ]$$\r\n \r\n \r\n q\r\n ∈\r\n [\r\n 1\r\n ,\r\n ∞\r\n ]\r\n \r\n \r\n \r\n satisfy \r\n \r\n $$\\frac{1}{p}+\\frac{1}{q}\\le \\frac{3}{2}$$\r\n \r\n \r\n \r\n 1\r\n p\r\n \r\n +\r\n \r\n 1\r\n q\r\n \r\n ≤\r\n \r\n 3\r\n 2\r\n \r\n \r\n \r\n \r\n , and on nonexistence if here \r\n \r\n $$p\\in [1,\\infty )$$\r\n \r\n \r\n p\r\n ∈\r\n [\r\n 1\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n \r\n and \r\n \r\n $$q\\in [1,\\infty )$$\r\n \r\n \r\n q\r\n ∈\r\n [\r\n 1\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n \r\n are such that \r\n \r\n $$\\frac{1}{p}+\\frac{1}{q}>\\frac{3}{2}$$\r\n \r\n \r\n \r\n 1\r\n p\r\n \r\n +\r\n \r\n 1\r\n q\r\n \r\n >\r\n \r\n 3\r\n 2\r\n \r\n \r\n \r\n \r\n .","lang":"eng"}],"status":"public","_id":"63248","user_id":"31496","language":[{"iso":"eng"}]},{"doi":"10.4171/aihpc/141","title":"Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system","date_created":"2025-12-18T19:00:24Z","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"volume":42,"date_updated":"2025-12-18T20:12:43Z","publisher":"European Mathematical Society - EMS - Publishing House GmbH","citation":{"chicago":"Winkler, Michael. “Logarithmically Refined Gagliardo–Nirenberg Interpolation and Application to Blow-up Exclusion in a Singular Chemotaxis–Consumption System.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 42, no. 6 (2024): 1601–30. https://doi.org/10.4171/aihpc/141.","ieee":"M. Winkler, “Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 42, no. 6, pp. 1601–1630, 2024, doi: 10.4171/aihpc/141.","ama":"Winkler M. Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 2024;42(6):1601-1630. doi:10.4171/aihpc/141","apa":"Winkler, M. (2024). Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 42(6), 1601–1630. https://doi.org/10.4171/aihpc/141","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 42 (2024) 1601–1630.","mla":"Winkler, Michael. “Logarithmically Refined Gagliardo–Nirenberg Interpolation and Application to Blow-up Exclusion in a Singular Chemotaxis–Consumption System.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, vol. 42, no. 6, European Mathematical Society - EMS - Publishing House GmbH, 2024, pp. 1601–30, doi:10.4171/aihpc/141.","bibtex":"@article{Winkler_2024, title={Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system}, volume={42}, DOI={10.4171/aihpc/141}, number={6}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2024}, pages={1601–1630} }"},"page":"1601-1630","intvolume":" 42","year":"2024","issue":"6","publication_status":"published","publication_identifier":{"issn":["0294-1449","1873-1430"]},"language":[{"iso":"eng"}],"user_id":"31496","_id":"63245","status":"public","abstract":[{"text":"\r\n A family of interpolation inequalities is derived, which differ from estimates of classical Gagliardo–Nirenberg type through the appearance of certain logarithmic deviations from standard Lebesgue norms in zero-order expressions. Optimality of the obtained inequalities is shown. A subsequent application reveals that when posed under homogeneous Neumann boundary conditions in smoothly bounded planar domains and with suitably regular initial data, for any choice of \r\n \r\n \\alpha>0\r\n \r\n the Keller–Segel-type migration–consumption system \r\n \r\n u_{t} = \\Delta (uv^{-\\alpha})\r\n \r\n , \r\n \r\n v_{t} = \\Delta v-uv\r\n \r\n , admits a global classical solution.\r\n ","lang":"eng"}],"type":"journal_article","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire"},{"abstract":[{"lang":"eng","text":"AbstractThe quasilinear Keller–Segel system$$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t=\\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (S(u)\\nabla v), \\\\ v_t=\\Delta v-v+u, \\end{array}\\right. \\end{aligned}$$ut=∇·(D(u)∇u)-∇·(S(u)∇v),vt=Δv-v+u,endowed with homogeneous Neumann boundary conditions is considered in a bounded domain$$\\Omega \\subset {\\mathbb {R}}^n$$Ω⊂Rn,$$n \\ge 3$$n≥3, with smooth boundary for sufficiently regular functionsDandSsatisfying$$D>0$$D>0on$$[0,\\infty )$$[0,∞),$$S>0$$S>0on$$(0,\\infty )$$(0,∞)and$$S(0)=0$$S(0)=0. On the one hand, it is shown that if$$\\frac{S}{D}$$SDsatisfies the subcritical growth condition$$\\begin{aligned} \\frac{S(s)}{D(s)} \\le C s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha < \\frac{2}{n} \\end{aligned}$$S(s)D(s)≤Csαforalls≥1withsomeα<2nand$$C>0$$C>0, then for any sufficiently regular initial data there exists a global weak energy solution such that$${ \\mathrm{{ess}}} \\sup _{t>0} \\Vert u(t) \\Vert _{L^p(\\Omega )}<\\infty $$esssupt>0‖u(t)‖Lp(Ω)<∞for some$$p > \\frac{2n}{n+2}$$p>2nn+2. On the other hand, if$$\\frac{S}{D}$$SDsatisfies the supercritical growth condition$$\\begin{aligned} \\frac{S(s)}{D(s)} \\ge c s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha > \\frac{2}{n} \\end{aligned}$$S(s)D(s)≥csαforalls≥1withsomeα>2nand$$c>0$$c>0, then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value$$\\alpha = \\frac{2}{n}$$α=2nfor$$n \\ge 3$$n≥3, without any additional assumption on the behavior ofD(s) as$$s \\rightarrow \\infty $$s→∞, in particular without requiring any algebraic lower bound forD. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type$$Q(s) = \\exp (-s^\\beta )$$Q(s)=exp(-sβ),$$s \\ge 0$$s≥0, for global solvability the exponent$$\\beta = \\frac{n-2}{n}$$β=n-2nis seen to be critical."}],"status":"public","publication":"Journal of Evolution Equations","type":"journal_article","article_number":"26","language":[{"iso":"eng"}],"_id":"63257","user_id":"31496","year":"2024","intvolume":" 24","citation":{"chicago":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” Journal of Evolution Equations 24, no. 2 (2024). https://doi.org/10.1007/s00028-024-00954-x.","ieee":"C. Stinner and M. Winkler, “A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects,” Journal of Evolution Equations, vol. 24, no. 2, Art. no. 26, 2024, doi: 10.1007/s00028-024-00954-x.","ama":"Stinner C, Winkler M. A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. Journal of Evolution Equations. 2024;24(2). doi:10.1007/s00028-024-00954-x","bibtex":"@article{Stinner_Winkler_2024, title={A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects}, volume={24}, DOI={10.1007/s00028-024-00954-x}, number={226}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Stinner, Christian and Winkler, Michael}, year={2024} }","mla":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” Journal of Evolution Equations, vol. 24, no. 2, 26, Springer Science and Business Media LLC, 2024, doi:10.1007/s00028-024-00954-x.","short":"C. Stinner, M. Winkler, Journal of Evolution Equations 24 (2024).","apa":"Stinner, C., & Winkler, M. (2024). A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. Journal of Evolution Equations, 24(2), Article 26. https://doi.org/10.1007/s00028-024-00954-x"},"publication_identifier":{"issn":["1424-3199","1424-3202"]},"publication_status":"published","issue":"2","title":"A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects","doi":"10.1007/s00028-024-00954-x","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:14:21Z","volume":24,"date_created":"2025-12-18T19:06:36Z","author":[{"first_name":"Christian","full_name":"Stinner, Christian","last_name":"Stinner"},{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}]},{"_id":"63253","user_id":"31496","article_number":"125006","language":[{"iso":"eng"}],"publication":"Nonlinearity","type":"journal_article","abstract":[{"text":"Abstract\r\n The Neumann problem for the Keller-Segel system \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n {\r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n ∇\r\n ⋅\r\n \r\n (\r\n D\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n u\r\n )\r\n \r\n −\r\n ∇\r\n ⋅\r\n \r\n (\r\n S\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n v\r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n −\r\n μ\r\n +\r\n u\r\n ,\r\n \r\n μ\r\n =\r\n \r\n −\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n u\r\n d\r\n x\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered in n-dimensional balls Ω with \r\n \r\n \r\n \r\n n\r\n ⩾\r\n 2\r\n \r\n \r\n , with suitably regular and radially symmetric, radially nonincreasing initial data u\r\n 0. The functions D and S are only assumed to belong to \r\n \r\n \r\n \r\n \r\n C\r\n 2\r\n \r\n (\r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n )\r\n \r\n \r\n and to satisfy D > 0 and \r\n \r\n \r\n \r\n S\r\n ⩾\r\n 0\r\n \r\n \r\n on \r\n \r\n \r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n as well as \r\n \r\n \r\n \r\n S\r\n (\r\n 0\r\n )\r\n =\r\n 0\r\n \r\n \r\n ; in particular, diffusivities with arbitrarily fast decay are included.\r\n In this general context, it is shown that it is merely the asymptotic behavior as \r\n \r\n \r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n of the expression \r\n \r\n \r\n \r\n \r\n \r\n \r\n I\r\n \r\n (\r\n ξ\r\n )\r\n \r\n :=\r\n \r\n \r\n S\r\n \r\n (\r\n ξ\r\n )\r\n \r\n \r\n \r\n \r\n ξ\r\n \r\n 2\r\n n\r\n \r\n \r\n D\r\n \r\n (\r\n ξ\r\n )\r\n \r\n \r\n \r\n ,\r\n \r\n ξ\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n which decides about the occurrence of blow-up: Namely, it is seen that\r\n\r\n \r\n •\r\n if \r\n \r\n \r\n \r\n \r\n lim\r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n I\r\n (\r\n ξ\r\n )\r\n =\r\n 0\r\n \r\n \r\n , then any such solution is global and bounded, that\r\n \r\n \r\n •\r\n if \r\n \r\n \r\n \r\n \r\n lim sup\r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n I\r\n (\r\n ξ\r\n )\r\n <\r\n ∞\r\n \r\n \r\n and \r\n \r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n u\r\n 0\r\n \r\n \r\n \r\n is suitably small, then the corresponding solution is global and bounded, and that\r\n \r\n \r\n •\r\n if \r\n \r\n \r\n \r\n \r\n lim inf\r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n I\r\n (\r\n ξ\r\n )\r\n >\r\n 0\r\n \r\n \r\n , then at each appropriately large mass level m, there exist radial initial data u\r\n 0 such that \r\n \r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n u\r\n 0\r\n \r\n =\r\n m\r\n \r\n \r\n , and that the associated solution blows up either in finite or in infinite time.\r\n \r\n \r\n \r\n This especially reveals the presence of critical mass phenomena whenever \r\n \r\n \r\n \r\n \r\n lim\r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n I\r\n (\r\n ξ\r\n )\r\n ∈\r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n exists.","lang":"eng"}],"status":"public","publisher":"IOP Publishing","date_updated":"2025-12-18T20:13:49Z","volume":37,"date_created":"2025-12-18T19:04:45Z","author":[{"full_name":"Ding, Mengyao","last_name":"Ding","first_name":"Mengyao"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"title":"Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture","doi":"10.1088/1361-6544/ad871a","publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","issue":"12","year":"2024","intvolume":" 37","citation":{"chicago":"Ding, Mengyao, and Michael Winkler. “Radial Blow-up in Quasilinear Keller-Segel Systems: Approaching the Full Picture.” Nonlinearity 37, no. 12 (2024). https://doi.org/10.1088/1361-6544/ad871a.","ieee":"M. Ding and M. Winkler, “Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture,” Nonlinearity, vol. 37, no. 12, Art. no. 125006, 2024, doi: 10.1088/1361-6544/ad871a.","ama":"Ding M, Winkler M. Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture. Nonlinearity. 2024;37(12). doi:10.1088/1361-6544/ad871a","apa":"Ding, M., & Winkler, M. (2024). Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture. Nonlinearity, 37(12), Article 125006. https://doi.org/10.1088/1361-6544/ad871a","short":"M. Ding, M. Winkler, Nonlinearity 37 (2024).","bibtex":"@article{Ding_Winkler_2024, title={Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture}, volume={37}, DOI={10.1088/1361-6544/ad871a}, number={12125006}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Ding, Mengyao and Winkler, Michael}, year={2024} }","mla":"Ding, Mengyao, and Michael Winkler. “Radial Blow-up in Quasilinear Keller-Segel Systems: Approaching the Full Picture.” Nonlinearity, vol. 37, no. 12, 125006, IOP Publishing, 2024, doi:10.1088/1361-6544/ad871a."}},{"language":[{"iso":"eng"}],"article_number":"60","user_id":"31496","_id":"63254","status":"public","abstract":[{"text":"AbstractThe chemotaxis-Navier–Stokes system $$\\begin{aligned} \\left\\{ \\begin{array}{rcl} n_t+u\\cdot \\nabla n & =& \\Delta \\big (n c^{-\\alpha } \\big ), \\\\ c_t+ u\\cdot \\nabla c & =& \\Delta c -nc,\\\\ u_t + (u\\cdot \\nabla ) u & =& \\Delta u+\\nabla P + n\\nabla \\Phi , \\qquad \\nabla \\cdot u=0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n n\r\n t\r\n \r\n +\r\n u\r\n ·\r\n ∇\r\n n\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n \r\n (\r\n \r\n n\r\n \r\n c\r\n \r\n -\r\n α\r\n \r\n \r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n c\r\n t\r\n \r\n +\r\n u\r\n ·\r\n ∇\r\n c\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n c\r\n -\r\n n\r\n c\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n +\r\n \r\n (\r\n u\r\n ·\r\n ∇\r\n )\r\n \r\n u\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n u\r\n +\r\n ∇\r\n P\r\n +\r\n n\r\n ∇\r\n Φ\r\n ,\r\n \r\n ∇\r\n ·\r\n u\r\n =\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain $$\\Omega \\subset \\mathbb R^2$$\r\n \r\n Ω\r\n ⊂\r\n \r\n R\r\n 2\r\n \r\n \r\n . For all $$\\alpha > 0$$\r\n \r\n α\r\n >\r\n 0\r\n \r\n and all sufficiently regular $$\\Phi $$\r\n Φ\r\n , we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for u at a point in the proof when knowledge about n is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time $$L^p$$\r\n \r\n L\r\n p\r\n \r\n estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time $$L^2$$\r\n \r\n L\r\n 2\r\n \r\n norm of the force term raised to an arbitrary small power.","lang":"eng"}],"publication":"Journal of Mathematical Fluid Mechanics","type":"journal_article","doi":"10.1007/s00021-024-00899-8","title":"Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing","volume":26,"author":[{"first_name":"Mario","last_name":"Fuest","full_name":"Fuest, Mario"},{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-18T19:05:09Z","date_updated":"2025-12-18T20:13:58Z","publisher":"Springer Science and Business Media LLC","intvolume":" 26","citation":{"mla":"Fuest, Mario, and Michael Winkler. “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing.” Journal of Mathematical Fluid Mechanics, vol. 26, no. 4, 60, Springer Science and Business Media LLC, 2024, doi:10.1007/s00021-024-00899-8.","bibtex":"@article{Fuest_Winkler_2024, title={Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing}, volume={26}, DOI={10.1007/s00021-024-00899-8}, number={460}, journal={Journal of Mathematical Fluid Mechanics}, publisher={Springer Science and Business Media LLC}, author={Fuest, Mario and Winkler, Michael}, year={2024} }","short":"M. Fuest, M. Winkler, Journal of Mathematical Fluid Mechanics 26 (2024).","apa":"Fuest, M., & Winkler, M. (2024). Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing. Journal of Mathematical Fluid Mechanics, 26(4), Article 60. https://doi.org/10.1007/s00021-024-00899-8","ama":"Fuest M, Winkler M. Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing. Journal of Mathematical Fluid Mechanics. 2024;26(4). doi:10.1007/s00021-024-00899-8","ieee":"M. Fuest and M. Winkler, “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing,” Journal of Mathematical Fluid Mechanics, vol. 26, no. 4, Art. no. 60, 2024, doi: 10.1007/s00021-024-00899-8.","chicago":"Fuest, Mario, and Michael Winkler. “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing.” Journal of Mathematical Fluid Mechanics 26, no. 4 (2024). https://doi.org/10.1007/s00021-024-00899-8."},"year":"2024","issue":"4","publication_identifier":{"issn":["1422-6928","1422-6952"]},"publication_status":"published"},{"language":[{"iso":"eng"}],"article_number":"e12885","user_id":"31496","_id":"63259","status":"public","abstract":[{"lang":"eng","text":"AbstractIn a smoothly bounded two‐dimensional domain and for a given nondecreasing positive unbounded , for each and the inequality\r\nis shown to hold for any positive fulfilling\r\nThis is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over near its explosion time."}],"publication":"Journal of the London Mathematical Society","type":"journal_article","doi":"10.1112/jlms.12885","title":"An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system","volume":109,"date_created":"2025-12-18T19:07:25Z","author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_updated":"2025-12-18T20:14:39Z","publisher":"Wiley","intvolume":" 109","citation":{"apa":"Wang, Y., & Winkler, M. (2024). An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. Journal of the London Mathematical Society, 109(3), Article e12885. https://doi.org/10.1112/jlms.12885","mla":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” Journal of the London Mathematical Society, vol. 109, no. 3, e12885, Wiley, 2024, doi:10.1112/jlms.12885.","bibtex":"@article{Wang_Winkler_2024, title={An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={10.1112/jlms.12885}, number={3e12885}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }","short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).","ama":"Wang Y, Winkler M. An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. Journal of the London Mathematical Society. 2024;109(3). doi:10.1112/jlms.12885","ieee":"Y. Wang and M. Winkler, “An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” Journal of the London Mathematical Society, vol. 109, no. 3, Art. no. e12885, 2024, doi: 10.1112/jlms.12885.","chicago":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” Journal of the London Mathematical Society 109, no. 3 (2024). https://doi.org/10.1112/jlms.12885."},"year":"2024","issue":"3","publication_identifier":{"issn":["0024-6107","1469-7750"]},"publication_status":"published"},{"_id":"63258","user_id":"31496","language":[{"iso":"eng"}],"publication":"Proceedings of the American Mathematical Society","type":"journal_article","abstract":[{"lang":"eng","text":"

This manuscript studies a no-flux initial-boundary value problem for a four-component chemotaxis system that has been proposed as a model for the response of cytotoxic T-lymphocytes to a solid tumor. In contrast to classical Keller-Segel type situations focusing on two-component interplay of chemotaxing populations with a signal directly secreted by themselves, the presently considered system accounts for a certain indirect mechanism of attractant evolution. Despite the presence of a zero-order exciting nonlinearity of quadratic type that forms a core mathematical feature of the model, the manuscript asserts the global existence of classical solutions for initial data of arbitrary size in three-dimensional domains.

"}],"status":"public","publisher":"American Mathematical Society (AMS)","date_updated":"2025-12-18T20:14:30Z","volume":152,"author":[{"last_name":"Tao","full_name":"Tao, Youshan","first_name":"Youshan"},{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T19:07:03Z","title":"Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor","doi":"10.1090/proc/16867","publication_identifier":{"issn":["0002-9939","1088-6826"]},"publication_status":"published","issue":"10","year":"2024","page":"4325-4341","intvolume":" 152","citation":{"mla":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Chemotaxis System Modeling Immune Response to a Solid Tumor.” Proceedings of the American Mathematical Society, vol. 152, no. 10, American Mathematical Society (AMS), 2024, pp. 4325–41, doi:10.1090/proc/16867.","bibtex":"@article{Tao_Winkler_2024, title={Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor}, volume={152}, DOI={10.1090/proc/16867}, number={10}, journal={Proceedings of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Tao, Youshan and Winkler, Michael}, year={2024}, pages={4325–4341} }","short":"Y. Tao, M. Winkler, Proceedings of the American Mathematical Society 152 (2024) 4325–4341.","apa":"Tao, Y., & Winkler, M. (2024). Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor. Proceedings of the American Mathematical Society, 152(10), 4325–4341. https://doi.org/10.1090/proc/16867","ama":"Tao Y, Winkler M. Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor. Proceedings of the American Mathematical Society. 2024;152(10):4325-4341. doi:10.1090/proc/16867","chicago":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Chemotaxis System Modeling Immune Response to a Solid Tumor.” Proceedings of the American Mathematical Society 152, no. 10 (2024): 4325–41. https://doi.org/10.1090/proc/16867.","ieee":"Y. Tao and M. Winkler, “Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor,” Proceedings of the American Mathematical Society, vol. 152, no. 10, pp. 4325–4341, 2024, doi: 10.1090/proc/16867."}},{"publication":"Nonlinear Analysis","type":"journal_article","status":"public","_id":"63256","user_id":"31496","article_number":"113600","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0362-546X"]},"publication_status":"published","year":"2024","intvolume":" 247","citation":{"ama":"Nikolić V, Winkler M. <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation. Nonlinear Analysis. 2024;247. doi:10.1016/j.na.2024.113600","chicago":"Nikolić, Vanja, and Michael Winkler. “<mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\" Altimg=\"si15.Svg\" Display=\"inline\" Id=\"d1e25\"><mml:Msup><mml:Mrow><mml:Mi>L</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mi>∞</Mml:Mi></Mml:Mrow></Mml:Msup></Mml:Math> Blow-up in the Jordan–Moore–Gibson–Thompson Equation.” Nonlinear Analysis 247 (2024). https://doi.org/10.1016/j.na.2024.113600.","ieee":"V. Nikolić and M. Winkler, “<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation,” Nonlinear Analysis, vol. 247, Art. no. 113600, 2024, doi: 10.1016/j.na.2024.113600.","apa":"Nikolić, V., & Winkler, M. (2024). <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation. Nonlinear Analysis, 247, Article 113600. https://doi.org/10.1016/j.na.2024.113600","mla":"Nikolić, Vanja, and Michael Winkler. “<mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\" Altimg=\"si15.Svg\" Display=\"inline\" Id=\"d1e25\"><mml:Msup><mml:Mrow><mml:Mi>L</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mi>∞</Mml:Mi></Mml:Mrow></Mml:Msup></Mml:Math> Blow-up in the Jordan–Moore–Gibson–Thompson Equation.” Nonlinear Analysis, vol. 247, 113600, Elsevier BV, 2024, doi:10.1016/j.na.2024.113600.","short":"V. Nikolić, M. Winkler, Nonlinear Analysis 247 (2024).","bibtex":"@article{Nikolić_Winkler_2024, title={<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation}, volume={247}, DOI={10.1016/j.na.2024.113600}, number={113600}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Nikolić, Vanja and Winkler, Michael}, year={2024} }"},"publisher":"Elsevier BV","date_updated":"2025-12-18T20:14:12Z","volume":247,"author":[{"first_name":"Vanja","full_name":"Nikolić, Vanja","last_name":"Nikolić"},{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:06:09Z","title":"L∞ blow-up in the Jordan–Moore–Gibson–Thompson equation","doi":"10.1016/j.na.2024.113600"},{"volume":297,"author":[{"last_name":"Wang","full_name":"Wang, Yulan","first_name":"Yulan"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:07:48Z","date_updated":"2025-12-18T20:14:46Z","publisher":"Wiley","doi":"10.1002/mana.202300361","title":"A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities","issue":"6","publication_identifier":{"issn":["0025-584X","1522-2616"]},"publication_status":"published","intvolume":" 297","page":"2353-2364","citation":{"short":"Y. Wang, M. Winkler, Mathematische Nachrichten 297 (2024) 2353–2364.","bibtex":"@article{Wang_Winkler_2024, title={A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities}, volume={297}, DOI={10.1002/mana.202300361}, number={6}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024}, pages={2353–2364} }","mla":"Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type Parabolic System Involving Density‐suppressed Motilities.” Mathematische Nachrichten, vol. 297, no. 6, Wiley, 2024, pp. 2353–64, doi:10.1002/mana.202300361.","apa":"Wang, Y., & Winkler, M. (2024). A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities. Mathematische Nachrichten, 297(6), 2353–2364. https://doi.org/10.1002/mana.202300361","ieee":"Y. Wang and M. Winkler, “A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities,” Mathematische Nachrichten, vol. 297, no. 6, pp. 2353–2364, 2024, doi: 10.1002/mana.202300361.","chicago":"Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type Parabolic System Involving Density‐suppressed Motilities.” Mathematische Nachrichten 297, no. 6 (2024): 2353–64. https://doi.org/10.1002/mana.202300361.","ama":"Wang Y, Winkler M. A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities. Mathematische Nachrichten. 2024;297(6):2353-2364. doi:10.1002/mana.202300361"},"year":"2024","user_id":"31496","_id":"63260","language":[{"iso":"eng"}],"publication":"Mathematische Nachrichten","type":"journal_article","status":"public","abstract":[{"text":"AbstractA no‐flux initial‐boundary value problem for\r\nis considered in a ball , where and .Under the assumption that , it is shown that for each , there exist and a positive with the property that whenever is nonnegative with , the global solutions to () emanating from the initial data have the property that\r\n","lang":"eng"}]},{"user_id":"31496","_id":"63262","language":[{"iso":"eng"}],"type":"journal_article","publication":"Israel Journal of Mathematics","status":"public","abstract":[{"lang":"eng","text":"AbstractRadially symmetric global unbounded solutions of the chemotaxis system $$\\left\\{ {\\matrix{{{u_t} = \\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (uS(u)\\nabla v),} \\hfill & {} \\hfill \\cr {0 = \\Delta v - \\mu + u,} \\hfill & {\\mu = {1 \\over {|\\Omega |}}\\int_\\Omega {u,} } \\hfill \\cr } } \\right.$$\r\n \r\n \r\n {\r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n ∇\r\n ⋅\r\n (\r\n D\r\n (\r\n u\r\n )\r\n ∇\r\n u\r\n )\r\n −\r\n ∇\r\n ⋅\r\n (\r\n u\r\n S\r\n (\r\n u\r\n )\r\n ∇\r\n v\r\n )\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n −\r\n μ\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n μ\r\n =\r\n \r\n 1\r\n \r\n |\r\n Ω\r\n |\r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n are considered in a ball Ω = BR(0) ⊂ ℝn, where n ≥ 3 and R > 0.Under the assumption that D and S suitably generalize the prototypes given by D(ξ) = (ξ + ι)m−1 and S(ξ) = (ξ + 1)−λ−1 for all ξ > 0 and some m ∈ ℝ, λ >0 and ι ≥ 0 fulfilling $$m + \\lambda < 1 - {2 \\over n}$$\r\n m\r\n +\r\n λ\r\n <\r\n 1\r\n −\r\n \r\n 2\r\n n\r\n \r\n , a considerably large set of initial data u0 is found to enforce a complete mass aggregation in infinite time in the sense that for any such u0, an associated Neumann type initial-boundary value problem admits a global classical solution (u, v) satisfying $${1 \\over C} \\cdot {(t + 1)^{{1 \\over \\lambda }}} \\le ||u( \\cdot ,t)|{|_{{L^\\infty }(\\Omega )}} \\le C \\cdot {(t + 1)^{{1 \\over \\lambda }}}\\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,t > 0$$\r\n \r\n \r\n 1\r\n C\r\n \r\n \r\n ⋅\r\n \r\n (\r\n t\r\n +\r\n 1\r\n \r\n )\r\n \r\n \r\n \r\n 1\r\n λ\r\n \r\n \r\n \r\n \r\n \r\n ≤\r\n \r\n |\r\n \r\n \r\n |\r\n \r\n u\r\n (\r\n ⋅\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n \r\n \r\n \r\n |\r\n \r\n \r\n \r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n ≤\r\n C\r\n ⋅\r\n \r\n (\r\n t\r\n +\r\n 1\r\n \r\n )\r\n \r\n \r\n \r\n 1\r\n λ\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n f\r\n o\r\n r\r\n \r\n \r\n \r\n \r\n \r\n \r\n a\r\n l\r\n l\r\n \r\n \r\n \r\n \r\n t\r\n >\r\n 0\r\n as well as $$||u( \\cdot \\,,t)|{|_{{L^1}(\\Omega \\backslash {B_{{r_0}}}(0))}} \\to 0\\,\\,\\,{\\rm{as}}\\,\\,t \\to \\infty \\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,{r_0} \\in (0,R)$$\r\n |\r\n |\r\n u\r\n (\r\n ⋅\r\n ,\r\n t\r\n )\r\n |\r\n \r\n |\r\n \r\n \r\n L\r\n 1\r\n \r\n (\r\n Ω\r\n \\\r\n \r\n B\r\n \r\n \r\n r\r\n 0\r\n \r\n \r\n \r\n (\r\n 0\r\n )\r\n )\r\n \r\n \r\n →\r\n 0\r\n as\r\n t\r\n →\r\n ∞\r\n for all\r\n \r\n r\r\n 0\r\n \r\n ∈\r\n (\r\n 0\r\n ,\r\n R\r\n )\r\n with some C > 0."}],"author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:08:34Z","volume":263,"publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:14:59Z","doi":"10.1007/s11856-024-2618-9","title":"Complete infinite-time mass aggregation in a quasilinear Keller–Segel system","issue":"1","publication_status":"published","publication_identifier":{"issn":["0021-2172","1565-8511"]},"citation":{"apa":"Winkler, M. (2024). Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. Israel Journal of Mathematics, 263(1), 93–127. https://doi.org/10.1007/s11856-024-2618-9","mla":"Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear Keller–Segel System.” Israel Journal of Mathematics, vol. 263, no. 1, Springer Science and Business Media LLC, 2024, pp. 93–127, doi:10.1007/s11856-024-2618-9.","short":"M. Winkler, Israel Journal of Mathematics 263 (2024) 93–127.","bibtex":"@article{Winkler_2024, title={Complete infinite-time mass aggregation in a quasilinear Keller–Segel system}, volume={263}, DOI={10.1007/s11856-024-2618-9}, number={1}, journal={Israel Journal of Mathematics}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2024}, pages={93–127} }","ama":"Winkler M. Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. Israel Journal of Mathematics. 2024;263(1):93-127. doi:10.1007/s11856-024-2618-9","ieee":"M. Winkler, “Complete infinite-time mass aggregation in a quasilinear Keller–Segel system,” Israel Journal of Mathematics, vol. 263, no. 1, pp. 93–127, 2024, doi: 10.1007/s11856-024-2618-9.","chicago":"Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear Keller–Segel System.” Israel Journal of Mathematics 263, no. 1 (2024): 93–127. https://doi.org/10.1007/s11856-024-2618-9."},"page":"93-127","intvolume":" 263","year":"2024"},{"status":"public","publication":"Journal of Differential Equations","type":"journal_article","language":[{"iso":"eng"}],"user_id":"31496","_id":"63263","intvolume":" 400","page":"423-456","citation":{"short":"M. Winkler, Journal of Differential Equations 400 (2024) 423–456.","mla":"Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient Taxis System with General Cross-Diffusive Flux.” Journal of Differential Equations, vol. 400, Elsevier BV, 2024, pp. 423–56, doi:10.1016/j.jde.2024.04.028.","bibtex":"@article{Winkler_2024, title={L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux}, volume={400}, DOI={10.1016/j.jde.2024.04.028}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2024}, pages={423–456} }","apa":"Winkler, M. (2024). L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux. Journal of Differential Equations, 400, 423–456. https://doi.org/10.1016/j.jde.2024.04.028","ama":"Winkler M. L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux. Journal of Differential Equations. 2024;400:423-456. doi:10.1016/j.jde.2024.04.028","ieee":"M. Winkler, “L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux,” Journal of Differential Equations, vol. 400, pp. 423–456, 2024, doi: 10.1016/j.jde.2024.04.028.","chicago":"Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient Taxis System with General Cross-Diffusive Flux.” Journal of Differential Equations 400 (2024): 423–56. https://doi.org/10.1016/j.jde.2024.04.028."},"year":"2024","publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","doi":"10.1016/j.jde.2024.04.028","title":"L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux","volume":400,"date_created":"2025-12-18T19:09:07Z","author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"publisher":"Elsevier BV","date_updated":"2025-12-18T20:15:05Z"},{"status":"public","type":"journal_article","article_number":"23945","article_type":"original","_id":"54815","user_id":"78890","department":[{"_id":"15"},{"_id":"623"},{"_id":"288"}],"citation":{"ama":"Pollmann R, Roeder F, Quiring V, et al. Integrated, bright broadband, two-colour parametric down-conversion source. Optics Express. 2024;32(14). doi:10.1364/oe.522549","chicago":"Pollmann, René, Franz Roeder, Victor Quiring, Raimund Ricken, Christof Eigner, Benjamin Brecht, and Christine Silberhorn. “Integrated, Bright Broadband, Two-Colour Parametric down-Conversion Source.” Optics Express 32, no. 14 (2024). https://doi.org/10.1364/oe.522549.","ieee":"R. Pollmann et al., “Integrated, bright broadband, two-colour parametric down-conversion source,” Optics Express, vol. 32, no. 14, Art. no. 23945, 2024, doi: 10.1364/oe.522549.","bibtex":"@article{Pollmann_Roeder_Quiring_Ricken_Eigner_Brecht_Silberhorn_2024, title={Integrated, bright broadband, two-colour parametric down-conversion source}, volume={32}, DOI={10.1364/oe.522549}, number={1423945}, journal={Optics Express}, publisher={Optica Publishing Group}, author={Pollmann, René and Roeder, Franz and Quiring, Victor and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}, year={2024} }","mla":"Pollmann, René, et al. “Integrated, Bright Broadband, Two-Colour Parametric down-Conversion Source.” Optics Express, vol. 32, no. 14, 23945, Optica Publishing Group, 2024, doi:10.1364/oe.522549.","short":"R. Pollmann, F. Roeder, V. Quiring, R. Ricken, C. Eigner, B. Brecht, C. Silberhorn, Optics Express 32 (2024).","apa":"Pollmann, R., Roeder, F., Quiring, V., Ricken, R., Eigner, C., Brecht, B., & Silberhorn, C. (2024). Integrated, bright broadband, two-colour parametric down-conversion source. Optics Express, 32(14), Article 23945. https://doi.org/10.1364/oe.522549"},"intvolume":" 32","publication_status":"published","publication_identifier":{"issn":["1094-4087"]},"doi":"10.1364/oe.522549","date_updated":"2025-12-19T11:37:41Z","author":[{"id":"78890","full_name":"Pollmann, René","last_name":"Pollmann","first_name":"René"},{"last_name":"Roeder","id":"88149","full_name":"Roeder, Franz","first_name":"Franz"},{"full_name":"Quiring, Victor","last_name":"Quiring","first_name":"Victor"},{"last_name":"Ricken","full_name":"Ricken, Raimund","first_name":"Raimund"},{"first_name":"Christof","full_name":"Eigner, Christof","id":"13244","orcid":"https://orcid.org/0000-0002-5693-3083","last_name":"Eigner"},{"full_name":"Brecht, Benjamin","id":"27150","last_name":"Brecht","orcid":"0000-0003-4140-0556 ","first_name":"Benjamin"},{"last_name":"Silberhorn","full_name":"Silberhorn, Christine","id":"26263","first_name":"Christine"}],"volume":32,"abstract":[{"lang":"eng","text":"Broadband quantum light is a vital resource for quantum metrology and spectroscopy applications such as quantum optical coherence tomography or entangled two photon absorption. For entangled two photon absorption in particular, very high photon flux combined with high time-frequency entanglement is crucial for observing a signal. So far these conditions could be met by using high power lasers driving degenerate, type 0 bulk-crystal spontaneous parametric down conversion (SPDC) sources. This naturally limits the available wavelength ranges and precludes deterministic splitting of the generated output photons. In this work we demonstrate an integrated two-colour SPDC source utilising a group-velocity matched lithium niobate waveguide, reaching both exceptional brightness 1.52⋅106pairssmWGHz and large bandwidth (7.8 THz FWHM) while pumped with a few mW of continuous wave (CW) laser light. By converting a narrow band pump to broadband pulses the created photon pairs show correlation times of Δτ ≈ 120 fs while maintaining the narrow bandwidth Δω\r\n p\r\n  ≪ 1 MHz of the CW pump light, yielding strong time-frequency entanglement. Furthermore our process can be adapted to a wide range of central wavelengths."}],"publication":"Optics Express","language":[{"iso":"eng"}],"year":"2024","issue":"14","title":"Integrated, bright broadband, two-colour parametric down-conversion source","publisher":"Optica Publishing Group","date_created":"2024-06-19T06:58:17Z"},{"doi":"10.1088/1367-2630/ad9f98","title":"Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared","volume":26,"author":[{"first_name":"Franz","full_name":"Roeder, Franz","id":"88149","last_name":"Roeder"},{"first_name":"Abira","full_name":"Gnanavel, Abira","last_name":"Gnanavel"},{"first_name":"René","last_name":"Pollmann","id":"78890","full_name":"Pollmann, René"},{"first_name":"Olga","full_name":"Brecht, Olga","last_name":"Brecht"},{"id":"42777","full_name":"Stefszky, Michael","last_name":"Stefszky","first_name":"Michael"},{"first_name":"Laura","last_name":"Padberg","id":"40300","full_name":"Padberg, Laura"},{"full_name":"Eigner, Christof","id":"13244","orcid":"https://orcid.org/0000-0002-5693-3083","last_name":"Eigner","first_name":"Christof"},{"last_name":"Silberhorn","id":"26263","full_name":"Silberhorn, Christine","first_name":"Christine"},{"first_name":"Benjamin","orcid":"0000-0003-4140-0556 ","last_name":"Brecht","id":"27150","full_name":"Brecht, Benjamin"}],"date_created":"2024-12-27T19:01:14Z","publisher":"IOP Publishing","date_updated":"2025-12-19T11:36:36Z","intvolume":" 26","citation":{"chicago":"Roeder, Franz, Abira Gnanavel, René Pollmann, Olga Brecht, Michael Stefszky, Laura Padberg, Christof Eigner, Christine Silberhorn, and Benjamin Brecht. “Ultra-Broadband Non-Degenerate Guided-Wave Bi-Photon Source in the near and Mid-Infrared.” New Journal of Physics 26, no. 12 (2024). https://doi.org/10.1088/1367-2630/ad9f98.","ieee":"F. Roeder et al., “Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared,” New Journal of Physics, vol. 26, no. 12, Art. no. 123025, 2024, doi: 10.1088/1367-2630/ad9f98.","ama":"Roeder F, Gnanavel A, Pollmann R, et al. Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared. New Journal of Physics. 2024;26(12). doi:10.1088/1367-2630/ad9f98","apa":"Roeder, F., Gnanavel, A., Pollmann, R., Brecht, O., Stefszky, M., Padberg, L., Eigner, C., Silberhorn, C., & Brecht, B. (2024). Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared. New Journal of Physics, 26(12), Article 123025. https://doi.org/10.1088/1367-2630/ad9f98","short":"F. Roeder, A. Gnanavel, R. Pollmann, O. Brecht, M. Stefszky, L. Padberg, C. Eigner, C. Silberhorn, B. Brecht, New Journal of Physics 26 (2024).","mla":"Roeder, Franz, et al. “Ultra-Broadband Non-Degenerate Guided-Wave Bi-Photon Source in the near and Mid-Infrared.” New Journal of Physics, vol. 26, no. 12, 123025, IOP Publishing, 2024, doi:10.1088/1367-2630/ad9f98.","bibtex":"@article{Roeder_Gnanavel_Pollmann_Brecht_Stefszky_Padberg_Eigner_Silberhorn_Brecht_2024, title={Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared}, volume={26}, DOI={10.1088/1367-2630/ad9f98}, number={12123025}, journal={New Journal of Physics}, publisher={IOP Publishing}, author={Roeder, Franz and Gnanavel, Abira and Pollmann, René and Brecht, Olga and Stefszky, Michael and Padberg, Laura and Eigner, Christof and Silberhorn, Christine and Brecht, Benjamin}, year={2024} }"},"year":"2024","issue":"12","publication_identifier":{"issn":["1367-2630"]},"publication_status":"published","language":[{"iso":"eng"}],"article_number":"123025","article_type":"original","department":[{"_id":"288"},{"_id":"623"},{"_id":"15"}],"user_id":"78890","_id":"57862","project":[{"name":"MIRAQLS: MIRAQLS: Mid-infrared Quantum Technology for Sensing","_id":"571"},{"_id":"190","name":"E2TPA: Exploiting Entangled Two-Photon Absorption"}],"status":"public","abstract":[{"lang":"eng","text":"The latest applications in ultrafast quantum metrology require bright, broadband bi-photon sources with one of the photons in the mid-infrared and the other in the visible to near infrared. However, existing sources based on bulk crystals are limited in brightness due to the short interaction length and only allow for limited dispersion engineering. Here, we present an integrated PDC source based on a Ti:LiNbO3 waveguide that generates broadband bi-photons with central wavelengths at 860 nm and 2800 nm. Their spectral bandwidth exceeds 25 THz and is achieved by simultaneous matching of the group velocities (GVs) and cancellation of GV dispersion for the signal and idler field. We provide an intuitive understanding of the process by studying our source’s behavior at different temperatures and pump wavelengths, which agrees well with simulations."}],"publication":"New Journal of Physics","type":"journal_article"},{"date_updated":"2025-12-22T10:40:28Z","volume":238,"author":[{"last_name":"Borgert","full_name":"Borgert, Thomas","id":"83141","first_name":"Thomas"},{"full_name":"Köhler, D","last_name":"Köhler","first_name":"D"},{"first_name":"Eugen","last_name":"Wiens","full_name":"Wiens, Eugen","id":"7888"},{"full_name":"Kupfer, R","last_name":"Kupfer","first_name":"R"},{"last_name":"Troschitz","full_name":"Troschitz, J","first_name":"J"},{"id":"233","full_name":"Homberg, Werner","last_name":"Homberg","first_name":"Werner"},{"full_name":"Gude, M","last_name":"Gude","first_name":"M"}],"doi":"10.1177/14644207241232233","publication_identifier":{"issn":["1464-4207","2041-3076"]},"publication_status":"published","page":"2299-2306","intvolume":" 238","citation":{"ama":"Borgert T, Köhler D, Wiens E, et al. In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications. 2024;238(12):2299-2306. doi:10.1177/14644207241232233","ieee":"T. Borgert et al., “In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element,” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, vol. 238, no. 12, pp. 2299–2306, 2024, doi: 10.1177/14644207241232233.","chicago":"Borgert, Thomas, D Köhler, Eugen Wiens, R Kupfer, J Troschitz, Werner Homberg, and M Gude. “In-Situ Computed Tomography Analysis of the Failure Mechanisms of Thermomechanically Manufactured Joints with Auxiliary Joining Element.” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 238, no. 12 (2024): 2299–2306. https://doi.org/10.1177/14644207241232233.","apa":"Borgert, T., Köhler, D., Wiens, E., Kupfer, R., Troschitz, J., Homberg, W., & Gude, M. (2024). In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 238(12), 2299–2306. https://doi.org/10.1177/14644207241232233","mla":"Borgert, Thomas, et al. “In-Situ Computed Tomography Analysis of the Failure Mechanisms of Thermomechanically Manufactured Joints with Auxiliary Joining Element.” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, vol. 238, no. 12, SAGE Publications, 2024, pp. 2299–306, doi:10.1177/14644207241232233.","short":"T. Borgert, D. Köhler, E. Wiens, R. Kupfer, J. Troschitz, W. Homberg, M. Gude, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 238 (2024) 2299–2306.","bibtex":"@article{Borgert_Köhler_Wiens_Kupfer_Troschitz_Homberg_Gude_2024, title={In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element}, volume={238}, DOI={10.1177/14644207241232233}, number={12}, journal={Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications}, publisher={SAGE Publications}, author={Borgert, Thomas and Köhler, D and Wiens, Eugen and Kupfer, R and Troschitz, J and Homberg, Werner and Gude, M}, year={2024}, pages={2299–2306} }"},"_id":"63346","department":[{"_id":"156"}],"user_id":"7888","type":"journal_article","status":"public","publisher":"SAGE Publications","date_created":"2025-12-19T09:13:30Z","title":"In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element","quality_controlled":"1","issue":"12","year":"2024","language":[{"iso":"eng"}],"publication":"Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications","abstract":[{"lang":"eng","text":" Lightweight design by using low-density and load-adapted materials can reduce the weight of vehicles and the emissions generated during operation. However, the usage of different materials requires innovative joining technologies with increased versatility. In this investigation, the focus is on describing and characterising the failure behaviour of connections manufactured by an innovative thermomechanical joining process with adaptable auxiliary joining elements in single-lap tensile-shear tests. In order to analyse the failure development in detail, the specimens are investigated using in-situ computed tomography (in-situ CT). Here, the tensile-shear test is interrupted at points of interest and CT scans are conducted under load. In addition, the interrupted in-situ testing procedure is validated by comparing the loading behaviour with conventional continuous tensile-shear tests. The results of the in-situ investigations of joints with varying material combinations clearly describe the cause of failure, allowing conclusions towards an improved joint design. "}]},{"has_accepted_license":"1","publication_status":"published","page":"1117–1120","citation":{"short":"O. Friesen, M.A. Pasha, M. Schwengelbeck, L. Claes, E. Baumhögger, B. Henning, in: Fortschritte der Akustik - DAGA 2024, 2024, pp. 1117–1120.","mla":"Friesen, Olga, et al. “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last.” Fortschritte der Akustik - DAGA 2024, 2024, pp. 1117–1120.","bibtex":"@inproceedings{Friesen_Pasha_Schwengelbeck_Claes_Baumhögger_Henning_2024, title={Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last}, booktitle={Fortschritte der Akustik - DAGA 2024}, author={Friesen, Olga and Pasha, Muhammad Ahsan and Schwengelbeck, Max and Claes, Leander and Baumhögger, Elmar and Henning, Bernd}, year={2024}, pages={1117–1120} }","apa":"Friesen, O., Pasha, M. A., Schwengelbeck, M., Claes, L., Baumhögger, E., & Henning, B. (2024). Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last. Fortschritte der Akustik - DAGA 2024, 1117–1120.","ieee":"O. Friesen, M. A. Pasha, M. Schwengelbeck, L. Claes, E. Baumhögger, and B. Henning, “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last,” in Fortschritte der Akustik - DAGA 2024, Hannover, 2024, pp. 1117–1120.","chicago":"Friesen, Olga, Muhammad Ahsan Pasha, Max Schwengelbeck, Leander Claes, Elmar Baumhögger, and Bernd Henning. “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last.” In Fortschritte der Akustik - DAGA 2024, 1117–1120, 2024.","ama":"Friesen O, Pasha MA, Schwengelbeck M, Claes L, Baumhögger E, Henning B. Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last. In: Fortschritte der Akustik - DAGA 2024. ; 2024:1117–1120."},"oa":"1","date_updated":"2026-01-05T07:56:21Z","author":[{"first_name":"Olga","last_name":"Friesen","full_name":"Friesen, Olga","id":"44026"},{"first_name":"Muhammad Ahsan","full_name":"Pasha, Muhammad Ahsan","last_name":"Pasha"},{"full_name":"Schwengelbeck, Max","last_name":"Schwengelbeck","first_name":"Max"},{"id":"11829","full_name":"Claes, Leander","last_name":"Claes","orcid":"0000-0002-4393-268X","first_name":"Leander"},{"first_name":"Elmar","full_name":"Baumhögger, Elmar","id":"15164","last_name":"Baumhögger"},{"last_name":"Henning","full_name":"Henning, Bernd","id":"213","first_name":"Bernd"}],"conference":{"start_date":"2024-03-18","name":"DAGA 2024 - 50. JAHRESTAGUNG FÜR AKUSTIK","location":"Hannover","end_date":"2024-03-21"},"type":"conference","status":"public","_id":"53822","project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"user_id":"11829","file_date_updated":"2024-05-02T14:07:24Z","year":"2024","date_created":"2024-05-02T13:25:29Z","title":"Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last","publication":"Fortschritte der Akustik - DAGA 2024","abstract":[{"lang":"ger","text":"Piezoelektrische Keramiken finden sowohl in Sensoren als auch in Aktoren Anwendung. Bei Hochleistungs-Ultraschallanwendungen sind diese Komponenten erheblichen elektrischen und mechanischen Belastungen ausgesetzt, was zum Auftreten nichtlinearer Effekte führt. Um das nichtlineare Materialverhalten piezoelektrischer Keramiken zu charakterisieren, kann eine statische mechanische Last aufgebracht werden, die den mechanischen Arbeitspunkt verschiebt. Durch Variation dieser statischen mechanischen Belastung kann das lineare Verhalten in jedem Betriebspunkt charakterisiert werden, woraufhin die nichtlinearen Eigenschaften des Materials angenähert werden können. Allerdings ist die Sicherstellung einer homogenen mechanischen Last anspruchsvoll. Alternativ kann eine hydrostatische Belastung realisiert werden, indem die Probe in einen Behälter gegeben wird, der mit unter Druck stehendem Fluid gefüllt ist. Dadurch wird eine gleichmäßige Lastverteilung über die Oberfläche der Probe erreicht.\r\n\r\nIn diesem Beitrag wird ein Versuchsaufbau zur Durchführung elektrischer Impedanzmessungen an piezoelektrischen Keramiken in einem Druckbehälter vorgestellt. Die Probe wird im Inneren des Druckbehälters elektrisch kontaktiert. Unter Verwendung von unter Druck stehendem Argon wird auf diese Weise die Messung der elektrischen Impedanz unter hydrostatischer Last von bis zu 200 bar ermöglicht. Anschließend wird ein inverses Verfahren angewendet, um die Materialparameter in Abhängigkeit von der aufgebrachten Last zu ermitteln."}],"file":[{"creator":"ofriesen","date_created":"2024-05-02T13:38:37Z","date_updated":"2024-05-02T14:07:24Z","file_id":"53826","access_level":"open_access","file_name":"daga2024friesen.pdf","file_size":453108,"content_type":"application/pdf","relation":"main_file"}],"ddc":["620"],"language":[{"iso":"ger"}]},{"publication":"Fortschritte der Akustik - DAGA 2024","type":"conference","status":"public","file":[{"date_updated":"2024-05-02T14:06:28Z","date_created":"2024-05-02T13:36:51Z","creator":"leanderc","file_size":365911,"access_level":"open_access","file_name":"daga2024koch.pdf","file_id":"53825","content_type":"application/pdf","relation":"main_file"}],"editor":[{"full_name":"Gesellschaft für Akustik e.V., Deutsche ","last_name":"Gesellschaft für Akustik e.V.","first_name":"Deutsche "}],"department":[{"_id":"49"}],"user_id":"11829","_id":"53824","project":[{"name":"ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"},{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"},{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"language":[{"iso":"ger"}],"file_date_updated":"2024-05-02T14:06:28Z","ddc":["620"],"has_accepted_license":"1","page":"1113–1116","citation":{"short":"K. Koch, L. Claes, B. Jurgelucks, L. Meihost, B. Henning, in: D. Gesellschaft für Akustik e.V. (Ed.), Fortschritte der Akustik - DAGA 2024, 2024, pp. 1113–1116.","bibtex":"@inproceedings{Koch_Claes_Jurgelucks_Meihost_Henning_2024, title={Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze}, booktitle={Fortschritte der Akustik - DAGA 2024}, author={Koch, Kevin and Claes, Leander and Jurgelucks, Benjamin and Meihost, Lars and Henning, Bernd}, editor={Gesellschaft für Akustik e.V., Deutsche }, year={2024}, pages={1113–1116} }","mla":"Koch, Kevin, et al. “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze.” Fortschritte der Akustik - DAGA 2024, edited by Deutsche Gesellschaft für Akustik e.V., 2024, pp. 1113–1116.","apa":"Koch, K., Claes, L., Jurgelucks, B., Meihost, L., & Henning, B. (2024). Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze. In D. Gesellschaft für Akustik e.V. (Ed.), Fortschritte der Akustik - DAGA 2024 (pp. 1113–1116).","ama":"Koch K, Claes L, Jurgelucks B, Meihost L, Henning B. Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze. In: Gesellschaft für Akustik e.V. D, ed. Fortschritte der Akustik - DAGA 2024. ; 2024:1113–1116.","chicago":"Koch, Kevin, Leander Claes, Benjamin Jurgelucks, Lars Meihost, and Bernd Henning. “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze.” In Fortschritte der Akustik - DAGA 2024, edited by Deutsche Gesellschaft für Akustik e.V., 1113–1116, 2024.","ieee":"K. Koch, L. Claes, B. Jurgelucks, L. Meihost, and B. Henning, “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze,” in Fortschritte der Akustik - DAGA 2024, 2024, pp. 1113–1116."},"year":"2024","author":[{"full_name":"Koch, Kevin","last_name":"Koch","first_name":"Kevin"},{"first_name":"Leander","id":"11829","full_name":"Claes, Leander","last_name":"Claes","orcid":"0000-0002-4393-268X"},{"last_name":"Jurgelucks","full_name":"Jurgelucks, Benjamin","first_name":"Benjamin"},{"full_name":"Meihost, Lars","id":"24769","last_name":"Meihost","first_name":"Lars"},{"full_name":"Henning, Bernd","id":"213","last_name":"Henning","first_name":"Bernd"}],"date_created":"2024-05-02T13:34:01Z","date_updated":"2026-01-05T07:56:42Z","oa":"1","conference":{"end_date":"2024-03-21","start_date":"2024-03-18"},"title":"Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze"},{"department":[{"_id":"49"}],"user_id":"11829","_id":"56834","project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"language":[{"iso":"eng"}],"publication":"2023 International Congress on Ultrasonics, Beijing, China","type":"conference","status":"public","volume":2822,"author":[{"first_name":"Olga","last_name":"Friesen","full_name":"Friesen, Olga","id":"44026"},{"first_name":"Leander","full_name":"Claes, Leander","id":"11829","orcid":"0000-0002-4393-268X","last_name":"Claes"},{"full_name":"Scheidemann, Claus","id":"38259","last_name":"Scheidemann","first_name":"Claus"},{"last_name":"Feldmann","id":"23082","full_name":"Feldmann, Nadine","first_name":"Nadine"},{"last_name":"Hemsel","full_name":"Hemsel, Tobias","id":"210","first_name":"Tobias"},{"last_name":"Henning","id":"213","full_name":"Henning, Bernd","first_name":"Bernd"}],"date_created":"2024-10-31T07:59:01Z","publisher":"IOP Publishing","date_updated":"2026-01-05T07:58:55Z","oa":"1","doi":"10.1088/1742-6596/2822/1/012125","main_file_link":[{"url":"https://iopscience.iop.org/article/10.1088/1742-6596/2822/1/012125","open_access":"1"}],"title":"Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens","publication_identifier":{"issn":["1742-6596"]},"intvolume":" 2822","page":"012125","citation":{"mla":"Friesen, Olga, et al. “Estimation of Temperature-Dependent Piezoelectric Material Parameters Using Ring-Shaped Specimens.” 2023 International Congress on Ultrasonics, Beijing, China, vol. 2822, IOP Publishing, 2024, p. 012125, doi:10.1088/1742-6596/2822/1/012125.","bibtex":"@inproceedings{Friesen_Claes_Scheidemann_Feldmann_Hemsel_Henning_2024, title={Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens}, volume={2822}, DOI={10.1088/1742-6596/2822/1/012125}, booktitle={2023 International Congress on Ultrasonics, Beijing, China}, publisher={IOP Publishing}, author={Friesen, Olga and Claes, Leander and Scheidemann, Claus and Feldmann, Nadine and Hemsel, Tobias and Henning, Bernd}, year={2024}, pages={012125} }","short":"O. Friesen, L. Claes, C. Scheidemann, N. Feldmann, T. Hemsel, B. Henning, in: 2023 International Congress on Ultrasonics, Beijing, China, IOP Publishing, 2024, p. 012125.","apa":"Friesen, O., Claes, L., Scheidemann, C., Feldmann, N., Hemsel, T., & Henning, B. (2024). Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens. 2023 International Congress on Ultrasonics, Beijing, China, 2822, 012125. https://doi.org/10.1088/1742-6596/2822/1/012125","ieee":"O. Friesen, L. Claes, C. Scheidemann, N. Feldmann, T. Hemsel, and B. Henning, “Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens,” in 2023 International Congress on Ultrasonics, Beijing, China, 2024, vol. 2822, p. 012125, doi: 10.1088/1742-6596/2822/1/012125.","chicago":"Friesen, Olga, Leander Claes, Claus Scheidemann, Nadine Feldmann, Tobias Hemsel, and Bernd Henning. “Estimation of Temperature-Dependent Piezoelectric Material Parameters Using Ring-Shaped Specimens.” In 2023 International Congress on Ultrasonics, Beijing, China, 2822:012125. IOP Publishing, 2024. https://doi.org/10.1088/1742-6596/2822/1/012125.","ama":"Friesen O, Claes L, Scheidemann C, Feldmann N, Hemsel T, Henning B. Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens. In: 2023 International Congress on Ultrasonics, Beijing, China. Vol 2822. IOP Publishing; 2024:012125. doi:10.1088/1742-6596/2822/1/012125"},"year":"2024"},{"type":"research_data","status":"public","user_id":"11829","department":[{"_id":"49"}],"project":[{"name":"ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"},{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"55470","citation":{"ama":"Koch K, Friesen O, Claes L. Randomised Material Parameter Impedance Dataset of Piezoelectric Rings. Zenodo; 2024. doi:10.5281/zenodo.13143680","ieee":"K. Koch, O. Friesen, and L. Claes, Randomised material parameter impedance dataset of piezoelectric rings. Zenodo, 2024.","chicago":"Koch, Kevin, Olga Friesen, and Leander Claes. Randomised Material Parameter Impedance Dataset of Piezoelectric Rings. Zenodo, 2024. https://doi.org/10.5281/zenodo.13143680.","short":"K. Koch, O. Friesen, L. Claes, Randomised Material Parameter Impedance Dataset of Piezoelectric Rings, Zenodo, 2024.","bibtex":"@book{Koch_Friesen_Claes_2024, title={Randomised material parameter impedance dataset of piezoelectric rings}, DOI={10.5281/zenodo.13143680}, publisher={Zenodo}, author={Koch, Kevin and Friesen, Olga and Claes, Leander}, year={2024} }","mla":"Koch, Kevin, et al. Randomised Material Parameter Impedance Dataset of Piezoelectric Rings. Zenodo, 2024, doi:10.5281/zenodo.13143680.","apa":"Koch, K., Friesen, O., & Claes, L. (2024). Randomised material parameter impedance dataset of piezoelectric rings. Zenodo. https://doi.org/10.5281/zenodo.13143680"},"year":"2024","date_created":"2024-07-31T14:10:12Z","author":[{"first_name":"Kevin","full_name":"Koch, Kevin","last_name":"Koch"},{"full_name":"Friesen, Olga","id":"44026","last_name":"Friesen","first_name":"Olga"},{"first_name":"Leander","full_name":"Claes, Leander","id":"11829","last_name":"Claes","orcid":"0000-0002-4393-268X"}],"publisher":"Zenodo","date_updated":"2026-01-05T07:57:46Z","doi":"10.5281/zenodo.13143680","title":"Randomised material parameter impedance dataset of piezoelectric rings"},{"status":"public","type":"research_data","user_id":"11829","department":[{"_id":"49"}],"project":[{"name":"ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"},{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"53662","citation":{"ieee":"K. Koch and L. Claes, Randomised material parameter piezoelectric impedance dataset with structured electrodes. zenodo, 2024.","chicago":"Koch, Kevin, and Leander Claes. Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes. zenodo, 2024. https://doi.org/10.5281/ZENODO.11064206.","ama":"Koch K, Claes L. Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes. zenodo; 2024. doi:10.5281/ZENODO.11064206","short":"K. Koch, L. Claes, Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes, zenodo, 2024.","mla":"Koch, Kevin, and Leander Claes. Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes. zenodo, 2024, doi:10.5281/ZENODO.11064206.","bibtex":"@book{Koch_Claes_2024, title={Randomised material parameter piezoelectric impedance dataset with structured electrodes}, DOI={10.5281/ZENODO.11064206}, publisher={zenodo}, author={Koch, Kevin and Claes, Leander}, year={2024} }","apa":"Koch, K., & Claes, L. (2024). Randomised material parameter piezoelectric impedance dataset with structured electrodes. zenodo. https://doi.org/10.5281/ZENODO.11064206"},"year":"2024","doi":"10.5281/ZENODO.11064206","title":"Randomised material parameter piezoelectric impedance dataset with structured electrodes","author":[{"full_name":"Koch, Kevin","last_name":"Koch","first_name":"Kevin"},{"first_name":"Leander","orcid":"0000-0002-4393-268X","last_name":"Claes","full_name":"Claes, Leander","id":"11829"}],"date_created":"2024-04-25T13:54:49Z","date_updated":"2026-01-05T07:56:58Z","publisher":"zenodo"}]