[{"volume":59,"doi":"10.1016/j.nonrwa.2020.103257","user_id":"31496","publisher":"Elsevier BV","_id":"63327","language":[{"iso":"eng"}],"article_number":"103257","intvolume":" 59","date_updated":"2025-12-18T19:59:57Z","publication_status":"published","publication_identifier":{"issn":["1468-1218"]},"author":[{"id":"31496","full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"year":"2020","status":"public","title":"Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with gradient-dependent flux limitation","type":"journal_article","date_created":"2025-12-18T19:36:51Z","citation":{"ieee":"M. Winkler, “Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with gradient-dependent flux limitation,” Nonlinear Analysis: Real World Applications, vol. 59, Art. no. 103257, 2020, doi: 10.1016/j.nonrwa.2020.103257.","apa":"Winkler, M. (2020). Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with gradient-dependent flux limitation. Nonlinear Analysis: Real World Applications, 59, Article 103257. https://doi.org/10.1016/j.nonrwa.2020.103257","short":"M. Winkler, Nonlinear Analysis: Real World Applications 59 (2020).","chicago":"Winkler, Michael. “Global Weak Solutions in a Three-Dimensional Keller–Segel–Navier–Stokes System with Gradient-Dependent Flux Limitation.” Nonlinear Analysis: Real World Applications 59 (2020). https://doi.org/10.1016/j.nonrwa.2020.103257.","mla":"Winkler, Michael. “Global Weak Solutions in a Three-Dimensional Keller–Segel–Navier–Stokes System with Gradient-Dependent Flux Limitation.” Nonlinear Analysis: Real World Applications, vol. 59, 103257, Elsevier BV, 2020, doi:10.1016/j.nonrwa.2020.103257.","bibtex":"@article{Winkler_2020, title={Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with gradient-dependent flux limitation}, volume={59}, DOI={10.1016/j.nonrwa.2020.103257}, number={103257}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2020} }","ama":"Winkler M. Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with gradient-dependent flux limitation. Nonlinear Analysis: Real World Applications. 2020;59. doi:10.1016/j.nonrwa.2020.103257"},"publication":"Nonlinear Analysis: Real World Applications"},{"type":"journal_article","date_created":"2025-12-18T19:39:40Z","publication":"Nonlinear Analysis","citation":{"ieee":"Y. Tao and M. Winkler, “A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy,” Nonlinear Analysis, vol. 198, Art. no. 111870, 2020, doi: 10.1016/j.na.2020.111870.","apa":"Tao, Y., & Winkler, M. (2020). A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Nonlinear Analysis, 198, Article 111870. https://doi.org/10.1016/j.na.2020.111870","short":"Y. Tao, M. Winkler, Nonlinear Analysis 198 (2020).","chicago":"Tao, Youshan, and Michael Winkler. “A Critical Virus Production Rate for Blow-up Suppression in a Haptotaxis Model for Oncolytic Virotherapy.” Nonlinear Analysis 198 (2020). https://doi.org/10.1016/j.na.2020.111870.","mla":"Tao, Youshan, and Michael Winkler. “A Critical Virus Production Rate for Blow-up Suppression in a Haptotaxis Model for Oncolytic Virotherapy.” Nonlinear Analysis, vol. 198, 111870, Elsevier BV, 2020, doi:10.1016/j.na.2020.111870.","bibtex":"@article{Tao_Winkler_2020, title={A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy}, volume={198}, DOI={10.1016/j.na.2020.111870}, number={111870}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2020} }","ama":"Tao Y, Winkler M. A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Nonlinear Analysis. 2020;198. doi:10.1016/j.na.2020.111870"},"doi":"10.1016/j.na.2020.111870","user_id":"31496","volume":198,"article_number":"111870","publisher":"Elsevier BV","_id":"63333","language":[{"iso":"eng"}],"date_updated":"2025-12-18T20:01:18Z","publication_status":"published","intvolume":" 198","status":"public","year":"2020","title":"A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy","publication_identifier":{"issn":["0362-546X"]},"author":[{"last_name":"Tao","first_name":"Youshan","full_name":"Tao, Youshan"},{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}]},{"article_number":"106785","publisher":"Elsevier BV","_id":"63328","language":[{"iso":"eng"}],"user_id":"31496","doi":"10.1016/j.aml.2020.106785","volume":112,"status":"public","year":"2020","title":"Boundedness in a three-dimensional Keller–Segel–Stokes system with subcritical sensitivity","author":[{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael","id":"31496"}],"publication_identifier":{"issn":["0893-9659"]},"publication_status":"published","date_updated":"2025-12-18T20:00:10Z","intvolume":" 112","date_created":"2025-12-18T19:37:32Z","type":"journal_article","publication":"Applied Mathematics Letters","citation":{"ama":"Winkler M. Boundedness in a three-dimensional Keller–Segel–Stokes system with subcritical sensitivity. Applied Mathematics Letters. 2020;112. doi:10.1016/j.aml.2020.106785","bibtex":"@article{Winkler_2020, title={Boundedness in a three-dimensional Keller–Segel–Stokes system with subcritical sensitivity}, volume={112}, DOI={10.1016/j.aml.2020.106785}, number={106785}, journal={Applied Mathematics Letters}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2020} }","mla":"Winkler, Michael. “Boundedness in a Three-Dimensional Keller–Segel–Stokes System with Subcritical Sensitivity.” Applied Mathematics Letters, vol. 112, 106785, Elsevier BV, 2020, doi:10.1016/j.aml.2020.106785.","chicago":"Winkler, Michael. “Boundedness in a Three-Dimensional Keller–Segel–Stokes System with Subcritical Sensitivity.” Applied Mathematics Letters 112 (2020). https://doi.org/10.1016/j.aml.2020.106785.","short":"M. Winkler, Applied Mathematics Letters 112 (2020).","apa":"Winkler, M. (2020). Boundedness in a three-dimensional Keller–Segel–Stokes system with subcritical sensitivity. Applied Mathematics Letters, 112, Article 106785. https://doi.org/10.1016/j.aml.2020.106785","ieee":"M. Winkler, “Boundedness in a three-dimensional Keller–Segel–Stokes system with subcritical sensitivity,” Applied Mathematics Letters, vol. 112, Art. no. 106785, 2020, doi: 10.1016/j.aml.2020.106785."}},{"page":"439-454","language":[{"iso":"eng"}],"_id":"63320","publisher":"American Institute of Mathematical Sciences (AIMS)","user_id":"31496","doi":"10.3934/dcds.2020216","volume":41,"status":"public","year":"2020","title":"Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction","publication_identifier":{"issn":["1553-5231"]},"author":[{"last_name":"Tao","first_name":"Youshan","full_name":"Tao, Youshan"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael","id":"31496"}],"publication_status":"published","date_updated":"2025-12-18T20:04:09Z","intvolume":" 41","date_created":"2025-12-18T19:33:59Z","type":"journal_article","publication":"Discrete & Continuous Dynamical Systems - A","issue":"1","citation":{"chicago":"Tao, Youshan, and Michael Winkler. “Critical Mass for Infinite-Time Blow-up in a Haptotaxis System with Nonlinear Zero-Order Interaction.” Discrete &amp; Continuous Dynamical Systems - A 41, no. 1 (2020): 439–54. https://doi.org/10.3934/dcds.2020216.","short":"Y. Tao, M. Winkler, Discrete &amp; Continuous Dynamical Systems - A 41 (2020) 439–454.","apa":"Tao, Y., & Winkler, M. (2020). Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete &amp; Continuous Dynamical Systems - A, 41(1), 439–454. https://doi.org/10.3934/dcds.2020216","ieee":"Y. Tao and M. Winkler, “Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction,” Discrete &amp; Continuous Dynamical Systems - A, vol. 41, no. 1, pp. 439–454, 2020, doi: 10.3934/dcds.2020216.","ama":"Tao Y, Winkler M. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete &amp; Continuous Dynamical Systems - A. 2020;41(1):439-454. doi:10.3934/dcds.2020216","bibtex":"@article{Tao_Winkler_2020, title={Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction}, volume={41}, DOI={10.3934/dcds.2020216}, number={1}, journal={Discrete &amp; Continuous Dynamical Systems - A}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Tao, Youshan and Winkler, Michael}, year={2020}, pages={439–454} }","mla":"Tao, Youshan, and Michael Winkler. “Critical Mass for Infinite-Time Blow-up in a Haptotaxis System with Nonlinear Zero-Order Interaction.” Discrete &amp; Continuous Dynamical Systems - A, vol. 41, no. 1, American Institute of Mathematical Sciences (AIMS), 2020, pp. 439–54, doi:10.3934/dcds.2020216."}},{"issue":"2","publication":"SIAM Journal on Mathematical Analysis","citation":{"bibtex":"@article{Winkler_2020, title={Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations}, volume={52}, DOI={10.1137/19m1264199}, number={2}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Winkler, Michael}, year={2020}, pages={2041–2080} }","ama":"Winkler M. Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations. SIAM Journal on Mathematical Analysis. 2020;52(2):2041-2080. doi:10.1137/19m1264199","mla":"Winkler, Michael. “Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations.” SIAM Journal on Mathematical Analysis, vol. 52, no. 2, Society for Industrial & Applied Mathematics (SIAM), 2020, pp. 2041–80, doi:10.1137/19m1264199.","short":"M. Winkler, SIAM Journal on Mathematical Analysis 52 (2020) 2041–2080.","chicago":"Winkler, Michael. “Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations.” SIAM Journal on Mathematical Analysis 52, no. 2 (2020): 2041–80. https://doi.org/10.1137/19m1264199.","ieee":"M. Winkler, “Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations,” SIAM Journal on Mathematical Analysis, vol. 52, no. 2, pp. 2041–2080, 2020, doi: 10.1137/19m1264199.","apa":"Winkler, M. (2020). Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations. SIAM Journal on Mathematical Analysis, 52(2), 2041–2080. https://doi.org/10.1137/19m1264199"},"type":"journal_article","date_created":"2025-12-18T19:40:35Z","publication_status":"published","date_updated":"2025-12-18T20:01:42Z","intvolume":" 52","status":"public","year":"2020","title":"Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations","publication_identifier":{"issn":["0036-1410","1095-7154"]},"author":[{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"user_id":"31496","doi":"10.1137/19m1264199","volume":52,"page":"2041-2080","_id":"63335","publisher":"Society for Industrial & Applied Mathematics (SIAM)","language":[{"iso":"eng"}]},{"abstract":[{"lang":"eng","text":"In a planar smoothly bounded domain$\\Omega$, we consider the model for oncolytic virotherapy given by$$\\left\\{ \\begin{array}{l} u_t = \\Delta u - \\nabla \\cdot (u\\nabla v) - uz, \\\\[1mm] v_t = - (u+w)v, \\\\[1mm] w_t = d_w \\Delta w - w + uz, \\\\[1mm] z_t = d_z \\Delta z - z - uz + \\beta w, \\end{array} \\right.$$with positive parameters$ D_w $,$ D_z $and$\\beta$. It is firstly shown that whenever$\\beta \\lt 1$, for any choice of$M \\gt 0$, one can find initial data such that the solution of an associated no-flux initial-boundary value problem, well known to exist globally actually for any choice of$\\beta \\gt 0$, satisfies$$u\\ge M \\qquad \\mbox{in } \\Omega\\times (0,\\infty).$$If$\\beta \\gt 1$, however, then for arbitrary initial data the corresponding is seen to have the property that$$\\liminf_{t\\to\\infty} \\inf_{x\\in\\Omega} u(x,t)\\le \\frac{1}{\\beta-1}.$$This may be interpreted as indicating that$\\beta$plays the role of a critical virus replication rate with regard to efficiency of the considered virotherapy, with corresponding threshold value given by$\\beta = 1$."}],"issue":"2","publication":"European Journal of Applied Mathematics","type":"journal_article","date_created":"2025-12-18T19:33:01Z","date_updated":"2025-12-18T20:06:35Z","publication_status":"published","intvolume":" 32","title":"A critical virus production rate for efficiency of oncolytic virotherapy","year":"2020","author":[{"full_name":"TAO, YOUSHAN","first_name":"YOUSHAN","last_name":"TAO"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"publication_identifier":{"issn":["0956-7925","1469-4425"]},"doi":"10.1017/s0956792520000133","language":[{"iso":"eng"}],"citation":{"short":"Y. TAO, M. Winkler, European Journal of Applied Mathematics 32 (2020) 301–316.","chicago":"TAO, YOUSHAN, and Michael Winkler. “A Critical Virus Production Rate for Efficiency of Oncolytic Virotherapy.” European Journal of Applied Mathematics 32, no. 2 (2020): 301–16. https://doi.org/10.1017/s0956792520000133.","apa":"TAO, Y., & Winkler, M. (2020). A critical virus production rate for efficiency of oncolytic virotherapy. European Journal of Applied Mathematics, 32(2), 301–316. https://doi.org/10.1017/s0956792520000133","ieee":"Y. TAO and M. Winkler, “A critical virus production rate for efficiency of oncolytic virotherapy,” European Journal of Applied Mathematics, vol. 32, no. 2, pp. 301–316, 2020, doi: 10.1017/s0956792520000133.","ama":"TAO Y, Winkler M. A critical virus production rate for efficiency of oncolytic virotherapy. European Journal of Applied Mathematics. 2020;32(2):301-316. doi:10.1017/s0956792520000133","bibtex":"@article{TAO_Winkler_2020, title={A critical virus production rate for efficiency of oncolytic virotherapy}, volume={32}, DOI={10.1017/s0956792520000133}, number={2}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={TAO, YOUSHAN and Winkler, Michael}, year={2020}, pages={301–316} }","mla":"TAO, YOUSHAN, and Michael Winkler. “A Critical Virus Production Rate for Efficiency of Oncolytic Virotherapy.” European Journal of Applied Mathematics, vol. 32, no. 2, Cambridge University Press (CUP), 2020, pp. 301–16, doi:10.1017/s0956792520000133."},"status":"public","user_id":"31496","volume":32,"page":"301-316","publisher":"Cambridge University Press (CUP)","_id":"63318"},{"type":"journal_article","date_created":"2025-12-18T19:31:21Z","abstract":[{"lang":"eng","text":"We propose and study a class of parabolic-ordinary differential equation models involving chemotaxis and haptotaxis of a species following signals indirectly produced by another, non-motile one. The setting is motivated by cancer invasion mediated by interactions with the tumour microenvironment, but has much wider applicability, being able to comprise descriptions of biologically quite different problems. As a main mathematical feature constituting a core difference to both classical Keller–Segel chemotaxis systems and Chaplain–Lolas type chemotaxis–haptotaxis systems, the considered model accounts for certain types of indirect signal production mechanisms. The main results assert unique global classical solvability under suitably mild assumptions on the system parameter functions in associated spatially two-dimensional initial-boundary value problems. In particular, this rigorously confirms that at least in two-dimensional settings, the considered indirectness in signal production induces a significant blow-up suppressing tendency also in taxis systems substantially more general than some particular examples for which corresponding effects have recently been observed."}],"issue":"4","publication":"European Journal of Applied Mathematics","doi":"10.1017/s0956792520000236","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-12-18T20:06:05Z","intvolume":" 32","title":"Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis–haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more)","year":"2020","author":[{"last_name":"SURULESCU","first_name":"CHRISTINA","full_name":"SURULESCU, CHRISTINA"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"publication_identifier":{"issn":["0956-7925","1469-4425"]},"citation":{"apa":"SURULESCU, C., & Winkler, M. (2020). Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis–haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more). European Journal of Applied Mathematics, 32(4), 618–651. https://doi.org/10.1017/s0956792520000236","ieee":"C. SURULESCU and M. Winkler, “Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis–haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more),” European Journal of Applied Mathematics, vol. 32, no. 4, pp. 618–651, 2020, doi: 10.1017/s0956792520000236.","short":"C. SURULESCU, M. Winkler, European Journal of Applied Mathematics 32 (2020) 618–651.","chicago":"SURULESCU, CHRISTINA, and Michael Winkler. “Does Indirectness of Signal Production Reduce the Explosion-Supporting Potential in Chemotaxis–Haptotaxis Systems? Global Classical Solvability in a Class of Models for Cancer Invasion (and More).” European Journal of Applied Mathematics 32, no. 4 (2020): 618–51. https://doi.org/10.1017/s0956792520000236.","mla":"SURULESCU, CHRISTINA, and Michael Winkler. “Does Indirectness of Signal Production Reduce the Explosion-Supporting Potential in Chemotaxis–Haptotaxis Systems? Global Classical Solvability in a Class of Models for Cancer Invasion (and More).” European Journal of Applied Mathematics, vol. 32, no. 4, Cambridge University Press (CUP), 2020, pp. 618–51, doi:10.1017/s0956792520000236.","ama":"SURULESCU C, Winkler M. Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis–haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more). European Journal of Applied Mathematics. 2020;32(4):618-651. doi:10.1017/s0956792520000236","bibtex":"@article{SURULESCU_Winkler_2020, title={Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis–haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more)}, volume={32}, DOI={10.1017/s0956792520000236}, number={4}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={SURULESCU, CHRISTINA and Winkler, Michael}, year={2020}, pages={618–651} }"},"user_id":"31496","volume":32,"page":"618-651","publisher":"Cambridge University Press (CUP)","_id":"63314","status":"public"},{"citation":{"chicago":"Winkler, Michael. “Approaching Critical Decay in a Strongly Degenerate Parabolic Equation.” Journal of Dynamics and Differential Equations 36, no. S1 (2020): 3–23. https://doi.org/10.1007/s10884-020-09892-x.","short":"M. Winkler, Journal of Dynamics and Differential Equations 36 (2020) 3–23.","apa":"Winkler, M. (2020). Approaching Critical Decay in a Strongly Degenerate Parabolic Equation. Journal of Dynamics and Differential Equations, 36(S1), 3–23. https://doi.org/10.1007/s10884-020-09892-x","ieee":"M. Winkler, “Approaching Critical Decay in a Strongly Degenerate Parabolic Equation,” Journal of Dynamics and Differential Equations, vol. 36, no. S1, pp. 3–23, 2020, doi: 10.1007/s10884-020-09892-x.","ama":"Winkler M. Approaching Critical Decay in a Strongly Degenerate Parabolic Equation. Journal of Dynamics and Differential Equations. 2020;36(S1):3-23. doi:10.1007/s10884-020-09892-x","bibtex":"@article{Winkler_2020, title={Approaching Critical Decay in a Strongly Degenerate Parabolic Equation}, volume={36}, DOI={10.1007/s10884-020-09892-x}, number={S1}, journal={Journal of Dynamics and Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2020}, pages={3–23} }","mla":"Winkler, Michael. “Approaching Critical Decay in a Strongly Degenerate Parabolic Equation.” Journal of Dynamics and Differential Equations, vol. 36, no. S1, Springer Science and Business Media LLC, 2020, pp. 3–23, doi:10.1007/s10884-020-09892-x."},"user_id":"31496","volume":36,"page":"3-23","_id":"63265","publisher":"Springer Science and Business Media LLC","status":"public","type":"journal_article","date_created":"2025-12-18T19:10:01Z","abstract":[{"text":"AbstractThe Cauchy problem in $${\\mathbb {R}}^n$$\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n , $$n\\ge 1$$\r\n \r\n n\r\n ≥\r\n 1\r\n \r\n , for the parabolic equation $$\\begin{aligned} u_t=u^p \\Delta u \\qquad \\qquad (\\star ) \\end{aligned}$$\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 u\r\n p\r\n \r\n Δ\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 \r\n is considered in the strongly degenerate regime $$p\\ge 1$$\r\n \r\n p\r\n ≥\r\n 1\r\n \r\n . The focus is firstly on the case of positive continuous and bounded initial data, in which it is known that a minimal positive classical solution exists, and that this solution satisfies $$\\begin{aligned} t^\\frac{1}{p}\\Vert u(\\cdot ,t)\\Vert _{L^\\infty ({\\mathbb {R}}^n)} \\rightarrow \\infty \\quad \\hbox {as } t\\rightarrow \\infty . \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n t\r\n \r\n 1\r\n p\r\n \r\n \r\n \r\n \r\n ‖\r\n u\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 L\r\n ∞\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n )\r\n \r\n \r\n \r\n →\r\n ∞\r\n \r\n as\r\n \r\n t\r\n →\r\n ∞\r\n .\r\n \r\n \r\n \r\n \r\n \r\n The first result of this study complements this by asserting that given any positive $$f\\in C^0([0,\\infty ))$$\r\n \r\n f\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 fulfilling $$f(t)\\rightarrow +\\infty $$\r\n \r\n f\r\n (\r\n t\r\n )\r\n →\r\n +\r\n ∞\r\n \r\n as $$t\\rightarrow \\infty $$\r\n \r\n t\r\n →\r\n ∞\r\n \r\n one can find a positive nondecreasing function $$\\phi \\in C^0([0,\\infty ))$$\r\n \r\n ϕ\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 such that whenever $$u_0\\in C^0({\\mathbb {R}}^n)$$\r\n \r\n \r\n u\r\n 0\r\n \r\n ∈\r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n )\r\n \r\n \r\n is radially symmetric with $$0< u_0 < \\phi (|\\cdot |)$$\r\n \r\n 0\r\n <\r\n \r\n u\r\n 0\r\n \r\n \r\n <\r\n ϕ\r\n (\r\n |\r\n \r\n ·\r\n \r\n |\r\n )\r\n \r\n \r\n , the corresponding minimal solution u satisfies $$\\begin{aligned} \\frac{t^\\frac{1}{p}\\Vert u(\\cdot ,t)\\Vert _{L^\\infty ({\\mathbb {R}}^n)}}{f(t)} \\rightarrow 0 \\quad \\hbox {as } t\\rightarrow \\infty . \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n t\r\n \r\n 1\r\n p\r\n \r\n \r\n \r\n \r\n ‖\r\n u\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 L\r\n ∞\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n f\r\n (\r\n t\r\n )\r\n \r\n \r\n →\r\n 0\r\n \r\n as\r\n \r\n t\r\n →\r\n ∞\r\n .\r\n \r\n \r\n \r\n \r\n \r\n Secondly, ($$\\star $$\r\n ⋆\r\n ) is considered along with initial conditions involving nonnegative but not necessarily strictly positive bounded and continuous initial data $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n . It is shown that if the connected components of $$\\{u_0>0\\}$$\r\n \r\n {\r\n \r\n u\r\n 0\r\n \r\n >\r\n 0\r\n }\r\n \r\n comply with a condition reflecting some uniform boundedness property, then a corresponding uniquely determined continuous weak solution to ($$\\star $$\r\n ⋆\r\n ) satisfies $$\\begin{aligned} 0< \\liminf _{t\\rightarrow \\infty } \\Big \\{ t^\\frac{1}{p} \\Vert u(\\cdot ,t)\\Vert _{L^\\infty ({\\mathbb {R}}^n)} \\Big \\} \\le \\limsup _{t\\rightarrow \\infty } \\Big \\{ t^\\frac{1}{p} \\Vert u(\\cdot ,t)\\Vert _{L^\\infty ({\\mathbb {R}}^n)} \\Big \\} <\\infty . \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n 0\r\n <\r\n \r\n lim inf\r\n \r\n t\r\n →\r\n ∞\r\n \r\n \r\n \r\n {\r\n \r\n \r\n t\r\n \r\n 1\r\n p\r\n \r\n \r\n \r\n \r\n ‖\r\n u\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 L\r\n ∞\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n )\r\n \r\n \r\n \r\n \r\n }\r\n \r\n ≤\r\n \r\n lim sup\r\n \r\n t\r\n →\r\n ∞\r\n \r\n \r\n \r\n {\r\n \r\n \r\n t\r\n \r\n 1\r\n p\r\n \r\n \r\n \r\n \r\n ‖\r\n u\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 L\r\n ∞\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n 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 \r\n \r\n \r\n Under a somewhat complementary hypothesis, particularly fulfilled if $$\\{u_0>0\\}$$\r\n \r\n {\r\n \r\n u\r\n 0\r\n \r\n >\r\n 0\r\n }\r\n \r\n contains components with arbitrarily small principal eigenvalues of the associated Dirichlet Laplacian, it is finally seen that (0.1) continues to hold also for such not everywhere positive weak solutions.","lang":"eng"}],"publication":"Journal of Dynamics and Differential Equations","issue":"S1","doi":"10.1007/s10884-020-09892-x","language":[{"iso":"eng"}],"date_updated":"2025-12-18T20:10:07Z","publication_status":"published","intvolume":" 36","title":"Approaching Critical Decay in a Strongly Degenerate Parabolic Equation","year":"2020","author":[{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"publication_identifier":{"issn":["1040-7294","1572-9222"]}},{"date_updated":"2026-01-05T07:53:10Z","publication_status":"published","author":[{"first_name":"Nadine","last_name":"Feldmann","full_name":"Feldmann, Nadine","id":"23082"},{"first_name":"Veronika","last_name":"Schulze","full_name":"Schulze, Veronika"},{"id":"11829","last_name":"Claes","first_name":"Leander","orcid":"0000-0002-4393-268X","full_name":"Claes, Leander"},{"first_name":"Benjamin","last_name":"Jurgelucks","full_name":"Jurgelucks, Benjamin"},{"first_name":"Andrea","last_name":"Walther","full_name":"Walther, Andrea"},{"full_name":"Henning, Bernd","first_name":"Bernd","last_name":"Henning","id":"213"}],"publication_identifier":{"issn":["2196-7113","0171-8096"]},"status":"public","year":"2020","title":"Inverse piezoelectric material parameter characterization using a single disc-shaped specimen","doi":"10.1515/teme-2020-0012","user_id":"11829","_id":"19313","language":[{"iso":"eng"}],"page":"50-55","project":[{"_id":"90","name":"Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"abstract":[{"lang":"eng","text":"The increasingly simulation-driven design process of ultrasonic transducers requires several reliable parameters for the description of the material behaviour. Exact results can only be achieved when a single specimen is used in the identification process, which typically is prone to the problem of low sensitivities to certain material parameters and thus high uncertainties. Therefore, a custom electrode topology for increased sensitivity is proposed for a piezoceramic disc. The thereupon conducted measurements of the electric impedance can be used as a starting point for an inverse approach where an equivalent simulation model is used to identify fitting material parameters. An optimisation strategy based on a preliminary sensitivity analysis is presented that leads to a good agreement between measurement and simulation. Furthermore, the proposed measurement procedure is able to evaluate the quality of the simulation model. Hence, different frequency-dependent damping models are presented and evaluated."}],"quality_controlled":"1","citation":{"ieee":"N. Feldmann, V. Schulze, L. Claes, B. Jurgelucks, A. Walther, and B. Henning, “Inverse piezoelectric material parameter characterization using a single disc-shaped specimen,” tm - Technisches Messen, pp. 50–55, 2020, doi: 10.1515/teme-2020-0012.","apa":"Feldmann, N., Schulze, V., Claes, L., Jurgelucks, B., Walther, A., & Henning, B. (2020). Inverse piezoelectric material parameter characterization using a single disc-shaped specimen. Tm - Technisches Messen, 50–55. https://doi.org/10.1515/teme-2020-0012","chicago":"Feldmann, Nadine, Veronika Schulze, Leander Claes, Benjamin Jurgelucks, Andrea Walther, and Bernd Henning. “Inverse Piezoelectric Material Parameter Characterization Using a Single Disc-Shaped Specimen.” Tm - Technisches Messen, 2020, 50–55. https://doi.org/10.1515/teme-2020-0012.","short":"N. Feldmann, V. Schulze, L. Claes, B. Jurgelucks, A. Walther, B. Henning, Tm - Technisches Messen (2020) 50–55.","mla":"Feldmann, Nadine, et al. “Inverse Piezoelectric Material Parameter Characterization Using a Single Disc-Shaped Specimen.” Tm - Technisches Messen, 2020, pp. 50–55, doi:10.1515/teme-2020-0012.","bibtex":"@article{Feldmann_Schulze_Claes_Jurgelucks_Walther_Henning_2020, title={Inverse piezoelectric material parameter characterization using a single disc-shaped specimen}, DOI={10.1515/teme-2020-0012}, journal={tm - Technisches Messen}, author={Feldmann, Nadine and Schulze, Veronika and Claes, Leander and Jurgelucks, Benjamin and Walther, Andrea and Henning, Bernd}, year={2020}, pages={50–55} }","ama":"Feldmann N, Schulze V, Claes L, Jurgelucks B, Walther A, Henning B. Inverse piezoelectric material parameter characterization using a single disc-shaped specimen. tm - Technisches Messen. Published online 2020:50-55. doi:10.1515/teme-2020-0012"},"publication":"tm - Technisches Messen","department":[{"_id":"49"}],"type":"journal_article","date_created":"2020-09-11T11:57:50Z"},{"date_updated":"2026-01-08T16:08:03Z","publication_status":"published","intvolume":" 7","title":"Plasmon-Driven Hot Electron Transfer at Atomically Sharp Metal–Semiconductor Nanojunctions","year":"2020","publication_identifier":{"issn":["2330-4022","2330-4022"]},"author":[{"first_name":"Masiar","last_name":"Sistani","full_name":"Sistani, Masiar"},{"full_name":"Bartmann, Maximilian G.","last_name":"Bartmann","first_name":"Maximilian G."},{"orcid":"0000-0002-4816-0666","first_name":"Nicholas Alexander","last_name":"Güsken","full_name":"Güsken, Nicholas Alexander","id":"112030"},{"full_name":"Oulton, Rupert F.","first_name":"Rupert F.","last_name":"Oulton"},{"last_name":"Keshmiri","first_name":"Hamid","full_name":"Keshmiri, Hamid"},{"full_name":"Luong, Minh Anh","first_name":"Minh Anh","last_name":"Luong"},{"full_name":"Momtaz, Zahra Sadre","last_name":"Momtaz","first_name":"Zahra Sadre"},{"full_name":"Den Hertog, Martien I.","last_name":"Den Hertog","first_name":"Martien I."},{"first_name":"Alois","last_name":"Lugstein","full_name":"Lugstein, Alois"}],"doi":"10.1021/acsphotonics.0c00557","language":[{"iso":"eng"}],"publication":"ACS Photonics","issue":"7","type":"journal_article","department":[{"_id":"623"},{"_id":"15"},{"_id":"230"}],"date_created":"2025-12-11T20:31:21Z","status":"public","user_id":"112030","volume":7,"page":"1642-1648","_id":"63038","publisher":"American Chemical Society (ACS)","citation":{"mla":"Sistani, Masiar, et al. “Plasmon-Driven Hot Electron Transfer at Atomically Sharp Metal–Semiconductor Nanojunctions.” ACS Photonics, vol. 7, no. 7, American Chemical Society (ACS), 2020, pp. 1642–48, doi:10.1021/acsphotonics.0c00557.","ama":"Sistani M, Bartmann MG, Güsken NA, et al. Plasmon-Driven Hot Electron Transfer at Atomically Sharp Metal–Semiconductor Nanojunctions. ACS Photonics. 2020;7(7):1642-1648. doi:10.1021/acsphotonics.0c00557","bibtex":"@article{Sistani_Bartmann_Güsken_Oulton_Keshmiri_Luong_Momtaz_Den Hertog_Lugstein_2020, title={Plasmon-Driven Hot Electron Transfer at Atomically Sharp Metal–Semiconductor Nanojunctions}, volume={7}, DOI={10.1021/acsphotonics.0c00557}, number={7}, journal={ACS Photonics}, publisher={American Chemical Society (ACS)}, author={Sistani, Masiar and Bartmann, Maximilian G. and Güsken, Nicholas Alexander and Oulton, Rupert F. and Keshmiri, Hamid and Luong, Minh Anh and Momtaz, Zahra Sadre and Den Hertog, Martien I. and Lugstein, Alois}, year={2020}, pages={1642–1648} }","apa":"Sistani, M., Bartmann, M. G., Güsken, N. A., Oulton, R. F., Keshmiri, H., Luong, M. A., Momtaz, Z. S., Den Hertog, M. I., & Lugstein, A. (2020). Plasmon-Driven Hot Electron Transfer at Atomically Sharp Metal–Semiconductor Nanojunctions. ACS Photonics, 7(7), 1642–1648. https://doi.org/10.1021/acsphotonics.0c00557","ieee":"M. Sistani et al., “Plasmon-Driven Hot Electron Transfer at Atomically Sharp Metal–Semiconductor Nanojunctions,” ACS Photonics, vol. 7, no. 7, pp. 1642–1648, 2020, doi: 10.1021/acsphotonics.0c00557.","short":"M. Sistani, M.G. Bartmann, N.A. Güsken, R.F. Oulton, H. Keshmiri, M.A. Luong, Z.S. Momtaz, M.I. Den Hertog, A. Lugstein, ACS Photonics 7 (2020) 1642–1648.","chicago":"Sistani, Masiar, Maximilian G. Bartmann, Nicholas Alexander Güsken, Rupert F. Oulton, Hamid Keshmiri, Minh Anh Luong, Zahra Sadre Momtaz, Martien I. Den Hertog, and Alois Lugstein. “Plasmon-Driven Hot Electron Transfer at Atomically Sharp Metal–Semiconductor Nanojunctions.” ACS Photonics 7, no. 7 (2020): 1642–48. https://doi.org/10.1021/acsphotonics.0c00557."}},{"status":"public","publisher":"American Chemical Society (ACS)","_id":"63042","page":"13872-13877","volume":124,"user_id":"112030","citation":{"short":"M. Sistani, M.G. Bartmann, N.A. Güsken, R.F. Oulton, H. Keshmiri, M.A. Luong, E. Robin, M.I. den Hertog, A. Lugstein, The Journal of Physical Chemistry C 124 (2020) 13872–13877.","chicago":"Sistani, Masiar, Maximilian G. Bartmann, Nicholas Alexander Güsken, Rupert F. Oulton, Hamid Keshmiri, Minh Anh Luong, Eric Robin, Martien I. den Hertog, and Alois Lugstein. “Stimulated Raman Scattering in Ge Nanowires.” The Journal of Physical Chemistry C 124, no. 25 (2020): 13872–77. https://doi.org/10.1021/acs.jpcc.0c02602.","apa":"Sistani, M., Bartmann, M. G., Güsken, N. A., Oulton, R. F., Keshmiri, H., Luong, M. A., Robin, E., den Hertog, M. I., & Lugstein, A. (2020). Stimulated Raman Scattering in Ge Nanowires. The Journal of Physical Chemistry C, 124(25), 13872–13877. https://doi.org/10.1021/acs.jpcc.0c02602","ieee":"M. Sistani et al., “Stimulated Raman Scattering in Ge Nanowires,” The Journal of Physical Chemistry C, vol. 124, no. 25, pp. 13872–13877, 2020, doi: 10.1021/acs.jpcc.0c02602.","ama":"Sistani M, Bartmann MG, Güsken NA, et al. Stimulated Raman Scattering in Ge Nanowires. The Journal of Physical Chemistry C. 2020;124(25):13872-13877. doi:10.1021/acs.jpcc.0c02602","bibtex":"@article{Sistani_Bartmann_Güsken_Oulton_Keshmiri_Luong_Robin_den Hertog_Lugstein_2020, title={Stimulated Raman Scattering in Ge Nanowires}, volume={124}, DOI={10.1021/acs.jpcc.0c02602}, number={25}, journal={The Journal of Physical Chemistry C}, publisher={American Chemical Society (ACS)}, author={Sistani, Masiar and Bartmann, Maximilian G. and Güsken, Nicholas Alexander and Oulton, Rupert F. and Keshmiri, Hamid and Luong, Minh Anh and Robin, Eric and den Hertog, Martien I. and Lugstein, Alois}, year={2020}, pages={13872–13877} }","mla":"Sistani, Masiar, et al. “Stimulated Raman Scattering in Ge Nanowires.” The Journal of Physical Chemistry C, vol. 124, no. 25, American Chemical Society (ACS), 2020, pp. 13872–77, doi:10.1021/acs.jpcc.0c02602."},"publication_identifier":{"issn":["1932-7447","1932-7455"]},"author":[{"last_name":"Sistani","first_name":"Masiar","full_name":"Sistani, Masiar"},{"full_name":"Bartmann, Maximilian G.","last_name":"Bartmann","first_name":"Maximilian G."},{"id":"112030","full_name":"Güsken, Nicholas Alexander","orcid":"0000-0002-4816-0666","last_name":"Güsken","first_name":"Nicholas Alexander"},{"full_name":"Oulton, Rupert F.","last_name":"Oulton","first_name":"Rupert F."},{"full_name":"Keshmiri, Hamid","first_name":"Hamid","last_name":"Keshmiri"},{"last_name":"Luong","first_name":"Minh Anh","full_name":"Luong, Minh Anh"},{"first_name":"Eric","last_name":"Robin","full_name":"Robin, Eric"},{"last_name":"den Hertog","first_name":"Martien I.","full_name":"den Hertog, Martien I."},{"last_name":"Lugstein","first_name":"Alois","full_name":"Lugstein, Alois"}],"title":"Stimulated Raman Scattering in Ge Nanowires","year":"2020","intvolume":" 124","date_updated":"2026-01-08T16:08:10Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1021/acs.jpcc.0c02602","publication":"The Journal of Physical Chemistry C","issue":"25","date_created":"2025-12-11T20:36:32Z","department":[{"_id":"623"},{"_id":"15"},{"_id":"230"}],"type":"journal_article"},{"title":"Erinnerungen als Lebensgeschichte. Zur ersten Biografie über Judith Kerr","status":"public","year":"2020","author":[{"full_name":"Jagdschian, Larissa Carolin","last_name":"Jagdschian","first_name":"Larissa Carolin","id":"105606"}],"date_updated":"2024-11-15T15:28:07Z","intvolume":" 72","page":"58-64","_id":"57114","language":[{"iso":"eng"}],"user_id":"105606","volume":72,"issue":"2","publication":"kjl&m","citation":{"mla":"Jagdschian, Larissa Carolin. “Erinnerungen Als Lebensgeschichte. Zur Ersten Biografie Über Judith Kerr.” Kjl&m, vol. 72, no. 2, 2020, pp. 58–64.","bibtex":"@article{Jagdschian_2020, title={Erinnerungen als Lebensgeschichte. Zur ersten Biografie über Judith Kerr}, volume={72}, number={2}, journal={kjl&m}, author={Jagdschian, Larissa Carolin}, year={2020}, pages={58–64} }","ama":"Jagdschian LC. Erinnerungen als Lebensgeschichte. Zur ersten Biografie über Judith Kerr. kjl&m. 2020;72(2):58-64.","ieee":"L. C. Jagdschian, “Erinnerungen als Lebensgeschichte. Zur ersten Biografie über Judith Kerr,” kjl&m, vol. 72, no. 2, pp. 58–64, 2020.","apa":"Jagdschian, L. C. (2020). Erinnerungen als Lebensgeschichte. Zur ersten Biografie über Judith Kerr. Kjl&m, 72(2), 58–64.","chicago":"Jagdschian, Larissa Carolin. “Erinnerungen Als Lebensgeschichte. Zur Ersten Biografie Über Judith Kerr.” Kjl&m 72, no. 2 (2020): 58–64.","short":"L.C. Jagdschian, Kjl&m 72 (2020) 58–64."},"date_created":"2024-11-15T15:27:56Z","type":"journal_article"},{"_id":"57074","language":[{"iso":"ger"}],"main_file_link":[{"url":"https://www.uni-paderborn.de/fileadmin/tevo/images_and_files/T.Evo_Abstract_DHd_2020_Spielraeume.pdf","open_access":"1"}],"user_id":"78730","author":[{"last_name":"Schuster","first_name":"Britt-Marie","full_name":"Schuster, Britt-Marie","id":"17386"},{"full_name":"Thielert, Frauke","last_name":"Thielert","first_name":"Frauke"},{"last_name":"Haaf","first_name":"Susanne","full_name":"Haaf, Susanne"},{"first_name":"Christopher","last_name":"Georgi","full_name":"Georgi, Christopher","id":"78730"}],"status":"public","title":"Merkmale registrieren oder textuelle Phänomene identifizieren? Zur Vereinbarkeit von automatischer und manueller Textsortenanalyse. Poster im Rahmen der DHd-Jahrestagung \"Spielräume\", März 2020, Paderborn","year":"2020","publication_status":"published","date_updated":"2024-11-13T16:05:06Z","date_created":"2024-11-13T16:03:12Z","department":[{"_id":"745"}],"oa":"1","type":"misc","citation":{"mla":"Schuster, Britt-Marie, et al. Merkmale registrieren oder textuelle Phänomene identifizieren? Zur Vereinbarkeit von automatischer und manueller Textsortenanalyse. Poster im Rahmen der DHd-Jahrestagung “Spielräume”, März 2020, Paderborn. 2020.","bibtex":"@book{Schuster_Thielert_Haaf_Georgi_2020, title={Merkmale registrieren oder textuelle Phänomene identifizieren? Zur Vereinbarkeit von automatischer und manueller Textsortenanalyse. Poster im Rahmen der DHd-Jahrestagung “Spielräume”, März 2020, Paderborn}, author={Schuster, Britt-Marie and Thielert, Frauke and Haaf, Susanne and Georgi, Christopher}, year={2020} }","ama":"Schuster B-M, Thielert F, Haaf S, Georgi C. 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