--- _id: '63264' abstract: - lang: eng 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]." author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 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 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} }' 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.' 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.' 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. date_created: 2025-12-18T19:09:41Z date_updated: 2025-12-18T20:10:00Z doi: 10.1515/ans-2023-0131 intvolume: ' 24' issue: '3' language: - iso: eng page: 592-615 publication: Advanced Nonlinear Studies publication_identifier: issn: - 2169-0375 publication_status: published publisher: Walter de Gruyter GmbH status: public title: A degenerate migration-consumption model in domains of arbitrary dimension type: journal_article user_id: '31496' volume: 24 year: '2024' ... --- _id: '63248' abstract: - lang: eng 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 \ ." author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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. date_created: 2025-12-18T19:02:09Z date_updated: 2025-12-18T20:13:05Z doi: 10.1007/s00208-024-02987-6 intvolume: ' 391' issue: '2' language: - iso: eng page: 3023-3054 publication: Mathematische Annalen publication_identifier: issn: - 0025-5831 - 1432-1807 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system type: journal_article user_id: '31496' volume: 391 year: '2024' ... --- _id: '63245' abstract: - lang: eng 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 " author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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} }' 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.' 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. short: M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 42 (2024) 1601–1630. date_created: 2025-12-18T19:00:24Z date_updated: 2025-12-18T20:12:43Z doi: 10.4171/aihpc/141 intvolume: ' 42' issue: '6' language: - iso: eng page: 1601-1630 publication: Annales de l'Institut Henri Poincaré C, Analyse non linéaire publication_identifier: issn: - 0294-1449 - 1873-1430 publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system type: journal_article user_id: '31496' volume: 42 year: '2024' ... --- _id: '63257' 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. article_number: '26' author: - first_name: Christian full_name: Stinner, Christian last_name: Stinner - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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). date_created: 2025-12-18T19:06:36Z date_updated: 2025-12-18T20:14:21Z doi: 10.1007/s00028-024-00954-x intvolume: ' 24' issue: '2' language: - iso: eng publication: Journal of Evolution Equations publication_identifier: issn: - 1424-3199 - 1424-3202 publication_status: published publisher: Springer Science and Business Media LLC status: public title: A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects type: journal_article user_id: '31496' volume: 24 year: '2024' ... --- _id: '63253' abstract: - lang: eng 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." article_number: '125006' author: - first_name: Mengyao full_name: Ding, Mengyao last_name: Ding - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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' 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} }' 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.' 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.' short: M. Ding, M. Winkler, Nonlinearity 37 (2024). date_created: 2025-12-18T19:04:45Z date_updated: 2025-12-18T20:13:49Z doi: 10.1088/1361-6544/ad871a intvolume: ' 37' issue: '12' language: - iso: eng publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published publisher: IOP Publishing status: public title: 'Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture' type: journal_article user_id: '31496' volume: 37 year: '2024' ... --- _id: '63254' abstract: - lang: eng 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." article_number: '60' author: - first_name: Mario full_name: Fuest, Mario last_name: Fuest - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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. 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.' 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. short: M. Fuest, M. Winkler, Journal of Mathematical Fluid Mechanics 26 (2024). date_created: 2025-12-18T19:05:09Z date_updated: 2025-12-18T20:13:58Z doi: 10.1007/s00021-024-00899-8 intvolume: ' 26' issue: '4' language: - iso: eng publication: Journal of Mathematical Fluid Mechanics publication_identifier: issn: - 1422-6928 - 1422-6952 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing type: journal_article user_id: '31496' volume: 26 year: '2024' ... --- _id: '63259' 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." article_number: e12885 author: - first_name: Yulan full_name: Wang, Yulan last_name: Wang - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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. 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.' 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. short: Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024). date_created: 2025-12-18T19:07:25Z date_updated: 2025-12-18T20:14:39Z doi: 10.1112/jlms.12885 intvolume: ' 109' issue: '3' language: - iso: eng publication: Journal of the London Mathematical Society publication_identifier: issn: - 0024-6107 - 1469-7750 publication_status: published publisher: Wiley status: public 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 type: journal_article user_id: '31496' volume: 109 year: '2024' ... --- _id: '63258' 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.

author: - first_name: Youshan full_name: Tao, Youshan last_name: Tao - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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. short: Y. Tao, M. Winkler, Proceedings of the American Mathematical Society 152 (2024) 4325–4341. date_created: 2025-12-18T19:07:03Z date_updated: 2025-12-18T20:14:30Z doi: 10.1090/proc/16867 intvolume: ' 152' issue: '10' language: - iso: eng page: 4325-4341 publication: Proceedings of the American Mathematical Society publication_identifier: issn: - 0002-9939 - 1088-6826 publication_status: published publisher: American Mathematical Society (AMS) status: public title: Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor type: journal_article user_id: '31496' volume: 152 year: '2024' ... --- _id: '63256' article_number: '113600' author: - first_name: Vanja full_name: Nikolić, Vanja last_name: Nikolić - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 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 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} }' 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.' 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). date_created: 2025-12-18T19:06:09Z date_updated: 2025-12-18T20:14:12Z doi: 10.1016/j.na.2024.113600 intvolume: ' 247' language: - iso: eng publication: Nonlinear Analysis publication_identifier: issn: - 0362-546X publication_status: published publisher: Elsevier BV status: public title: L∞ blow-up in the Jordan–Moore–Gibson–Thompson equation type: journal_article user_id: '31496' volume: 247 year: '2024' ... --- _id: '63260' abstract: - lang: eng 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" author: - first_name: Yulan full_name: Wang, Yulan last_name: Wang - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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.' 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. short: Y. Wang, M. Winkler, Mathematische Nachrichten 297 (2024) 2353–2364. date_created: 2025-12-18T19:07:48Z date_updated: 2025-12-18T20:14:46Z doi: 10.1002/mana.202300361 intvolume: ' 297' issue: '6' language: - iso: eng page: 2353-2364 publication: Mathematische Nachrichten publication_identifier: issn: - 0025-584X - 1522-2616 publication_status: published publisher: Wiley status: public title: A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities type: journal_article user_id: '31496' volume: 297 year: '2024' ... --- _id: '63262' 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: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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.' 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. date_created: 2025-12-18T19:08:34Z date_updated: 2025-12-18T20:14:59Z doi: 10.1007/s11856-024-2618-9 intvolume: ' 263' issue: '1' language: - iso: eng page: 93-127 publication: Israel Journal of Mathematics publication_identifier: issn: - 0021-2172 - 1565-8511 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Complete infinite-time mass aggregation in a quasilinear Keller–Segel system type: journal_article user_id: '31496' volume: 263 year: '2024' ... --- _id: '63263' author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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.' 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. short: M. Winkler, Journal of Differential Equations 400 (2024) 423–456. date_created: 2025-12-18T19:09:07Z date_updated: 2025-12-18T20:15:05Z doi: 10.1016/j.jde.2024.04.028 intvolume: ' 400' language: - iso: eng page: 423-456 publication: Journal of Differential Equations publication_identifier: issn: - 0022-0396 publication_status: published publisher: Elsevier BV status: public title: L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux type: journal_article user_id: '31496' volume: 400 year: '2024' ... --- _id: '54815' 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." article_number: '23945' article_type: original author: - first_name: René full_name: Pollmann, René id: '78890' last_name: Pollmann - first_name: Franz full_name: Roeder, Franz id: '88149' last_name: Roeder - first_name: Victor full_name: Quiring, Victor last_name: Quiring - first_name: Raimund full_name: Ricken, Raimund last_name: Ricken - first_name: Christof full_name: Eigner, Christof id: '13244' last_name: Eigner orcid: https://orcid.org/0000-0002-5693-3083 - first_name: Benjamin full_name: Brecht, Benjamin id: '27150' last_name: Brecht orcid: '0000-0003-4140-0556 ' - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn 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 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 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} }' 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.' 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). date_created: 2024-06-19T06:58:17Z date_updated: 2025-12-19T11:37:41Z department: - _id: '15' - _id: '623' - _id: '288' doi: 10.1364/oe.522549 intvolume: ' 32' issue: '14' language: - iso: eng publication: Optics Express publication_identifier: issn: - 1094-4087 publication_status: published publisher: Optica Publishing Group status: public title: Integrated, bright broadband, two-colour parametric down-conversion source type: journal_article user_id: '78890' volume: 32 year: '2024' ... --- _id: '57862' 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. article_number: '123025' article_type: original 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 full_name: Pollmann, René id: '78890' last_name: Pollmann - first_name: Olga full_name: Brecht, Olga last_name: Brecht - first_name: Michael full_name: Stefszky, Michael id: '42777' last_name: Stefszky - first_name: Laura full_name: Padberg, Laura id: '40300' last_name: Padberg - first_name: Christof full_name: Eigner, Christof id: '13244' last_name: Eigner orcid: https://orcid.org/0000-0002-5693-3083 - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn - first_name: Benjamin full_name: Brecht, Benjamin id: '27150' last_name: Brecht orcid: '0000-0003-4140-0556 ' citation: 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 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} }' 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.' 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. 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). date_created: 2024-12-27T19:01:14Z date_updated: 2025-12-19T11:36:36Z department: - _id: '288' - _id: '623' - _id: '15' doi: 10.1088/1367-2630/ad9f98 intvolume: ' 26' issue: '12' language: - iso: eng project: - _id: '571' name: 'MIRAQLS: MIRAQLS: Mid-infrared Quantum Technology for Sensing' - _id: '190' name: 'E2TPA: Exploiting Entangled Two-Photon Absorption' publication: New Journal of Physics publication_identifier: issn: - 1367-2630 publication_status: published publisher: IOP Publishing status: public title: Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared type: journal_article user_id: '78890' volume: 26 year: '2024' ... --- _id: '63346' 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. author: - first_name: Thomas full_name: Borgert, Thomas id: '83141' last_name: Borgert - first_name: D full_name: Köhler, D last_name: Köhler - first_name: Eugen full_name: Wiens, Eugen id: '7888' last_name: Wiens - first_name: R full_name: Kupfer, R last_name: Kupfer - first_name: J full_name: Troschitz, J last_name: Troschitz - first_name: Werner full_name: Homberg, Werner id: '233' last_name: Homberg - first_name: M full_name: Gude, M last_name: Gude 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' 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' 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} }' 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.' 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.' 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.' date_created: 2025-12-19T09:13:30Z date_updated: 2025-12-22T10:40:28Z department: - _id: '156' doi: 10.1177/14644207241232233 intvolume: ' 238' issue: '12' language: - iso: eng page: 2299-2306 publication: 'Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications' publication_identifier: issn: - 1464-4207 - 2041-3076 publication_status: published publisher: SAGE Publications quality_controlled: '1' status: public title: In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element type: journal_article user_id: '7888' volume: 238 year: '2024' ... --- _id: '53822' 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." author: - first_name: Olga full_name: Friesen, Olga id: '44026' last_name: Friesen - first_name: Muhammad Ahsan full_name: Pasha, Muhammad Ahsan last_name: Pasha - first_name: Max full_name: Schwengelbeck, Max last_name: Schwengelbeck - first_name: Leander full_name: Claes, Leander id: '11829' last_name: Claes orcid: 0000-0002-4393-268X - first_name: Elmar full_name: Baumhögger, Elmar id: '15164' last_name: Baumhögger - first_name: Bernd full_name: Henning, Bernd id: '213' last_name: Henning citation: 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.' 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. 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} }' 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. 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. mla: Friesen, Olga, et al. “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last.” Fortschritte der Akustik - DAGA 2024, 2024, pp. 1117–1120. short: 'O. Friesen, M.A. Pasha, M. Schwengelbeck, L. Claes, E. Baumhögger, B. Henning, in: Fortschritte der Akustik - DAGA 2024, 2024, pp. 1117–1120.' conference: end_date: 2024-03-21 location: Hannover name: DAGA 2024 - 50. JAHRESTAGUNG FÜR AKUSTIK start_date: 2024-03-18 date_created: 2024-05-02T13:25:29Z date_updated: 2026-01-05T07:56:21Z ddc: - '620' file: - access_level: open_access content_type: application/pdf creator: ofriesen date_created: 2024-05-02T13:38:37Z date_updated: 2024-05-02T14:07:24Z file_id: '53826' file_name: daga2024friesen.pdf file_size: 453108 relation: main_file file_date_updated: 2024-05-02T14:07:24Z has_accepted_license: '1' language: - iso: ger oa: '1' page: 1117–1120 project: - _id: '245' name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)' publication: Fortschritte der Akustik - DAGA 2024 publication_status: published status: public title: Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last type: conference user_id: '11829' year: '2024' ... --- _id: '53824' author: - first_name: Kevin full_name: Koch, Kevin last_name: Koch - first_name: Leander full_name: Claes, Leander id: '11829' last_name: Claes orcid: 0000-0002-4393-268X - first_name: Benjamin full_name: Jurgelucks, Benjamin last_name: Jurgelucks - first_name: Lars full_name: Meihost, Lars id: '24769' last_name: Meihost - first_name: Bernd full_name: Henning, Bernd id: '213' last_name: Henning citation: 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.' 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). 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} }' 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. 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. 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.' conference: end_date: 2024-03-21 start_date: 2024-03-18 date_created: 2024-05-02T13:34:01Z date_updated: 2026-01-05T07:56:42Z ddc: - '620' department: - _id: '49' editor: - first_name: 'Deutsche ' full_name: 'Gesellschaft für Akustik e.V., Deutsche ' last_name: Gesellschaft für Akustik e.V. file: - access_level: open_access content_type: application/pdf creator: leanderc date_created: 2024-05-02T13:36:51Z date_updated: 2024-05-02T14:06:28Z file_id: '53825' file_name: daga2024koch.pdf file_size: 365911 relation: main_file file_date_updated: 2024-05-02T14:06:28Z has_accepted_license: '1' language: - iso: ger oa: '1' page: 1113–1116 project: - _id: '90' name: 'ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums' - _id: '52' name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing' - _id: '245' name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)' publication: Fortschritte der Akustik - DAGA 2024 status: public title: Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze type: conference user_id: '11829' year: '2024' ... --- _id: '56834' author: - first_name: Olga full_name: Friesen, Olga id: '44026' last_name: Friesen - first_name: Leander full_name: Claes, Leander id: '11829' last_name: Claes orcid: 0000-0002-4393-268X - first_name: Claus full_name: Scheidemann, Claus id: '38259' last_name: Scheidemann - first_name: Nadine full_name: Feldmann, Nadine id: '23082' last_name: Feldmann - first_name: Tobias full_name: Hemsel, Tobias id: '210' last_name: Hemsel - first_name: Bernd full_name: Henning, Bernd id: '213' last_name: Henning citation: 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' 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 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} }' 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. 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.' 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. 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.' date_created: 2024-10-31T07:59:01Z date_updated: 2026-01-05T07:58:55Z department: - _id: '49' doi: 10.1088/1742-6596/2822/1/012125 intvolume: ' 2822' language: - iso: eng main_file_link: - open_access: '1' url: https://iopscience.iop.org/article/10.1088/1742-6596/2822/1/012125 oa: '1' page: '012125' project: - _id: '245' name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)' publication: 2023 International Congress on Ultrasonics, Beijing, China publication_identifier: issn: - 1742-6596 publisher: IOP Publishing status: public title: Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens type: conference user_id: '11829' volume: 2822 year: '2024' ... --- _id: '55470' author: - first_name: Kevin full_name: Koch, Kevin last_name: Koch - first_name: Olga full_name: Friesen, Olga id: '44026' last_name: Friesen - first_name: Leander full_name: Claes, Leander id: '11829' last_name: Claes orcid: 0000-0002-4393-268X citation: ama: Koch K, Friesen O, Claes L. 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 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} }' 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. ieee: K. Koch, O. Friesen, and L. Claes, Randomised material parameter impedance dataset of piezoelectric rings. Zenodo, 2024. mla: Koch, Kevin, et al. Randomised Material Parameter Impedance Dataset of Piezoelectric Rings. Zenodo, 2024, doi:10.5281/zenodo.13143680. short: K. Koch, O. Friesen, L. Claes, Randomised Material Parameter Impedance Dataset of Piezoelectric Rings, Zenodo, 2024. date_created: 2024-07-31T14:10:12Z date_updated: 2026-01-05T07:57:46Z department: - _id: '49' doi: 10.5281/zenodo.13143680 project: - _id: '90' name: 'ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums' - _id: '52' name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing' - _id: '245' name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)' publisher: Zenodo status: public title: Randomised material parameter impedance dataset of piezoelectric rings type: research_data user_id: '11829' year: '2024' ... --- _id: '53662' author: - first_name: Kevin full_name: Koch, Kevin last_name: Koch - first_name: Leander full_name: Claes, Leander id: '11829' last_name: Claes orcid: 0000-0002-4393-268X citation: ama: Koch K, Claes L. Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes. zenodo; 2024. doi:10.5281/ZENODO.11064206 apa: Koch, K., & Claes, L. (2024). Randomised material parameter piezoelectric impedance dataset with structured electrodes. zenodo. https://doi.org/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} }' chicago: Koch, Kevin, and Leander Claes. Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes. zenodo, 2024. https://doi.org/10.5281/ZENODO.11064206. ieee: K. Koch and 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. short: K. Koch, L. Claes, Randomised Material Parameter Piezoelectric Impedance Dataset with Structured Electrodes, zenodo, 2024. date_created: 2024-04-25T13:54:49Z date_updated: 2026-01-05T07:56:58Z department: - _id: '49' doi: 10.5281/ZENODO.11064206 project: - _id: '90' name: 'ChaMP: Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums' - _id: '52' name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing' - _id: '245' name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)' publisher: zenodo status: public title: Randomised material parameter piezoelectric impedance dataset with structured electrodes type: research_data user_id: '11829' year: '2024' ...