Edit Profile (opens in new tab) Winkler, Michael Co-Author Distance Author ID: winkler.michael Published as: Winkler, Michael; Winkler, M. Homepage: https://www2.math.uni-paderborn.de/?id=16819 External Links: MGP · ResearchGate · dblp · GND Documents Indexed: 253 Publications since 2001, including 10 Additional arXiv Preprints 3 Contributions as Editor Co-Authors: 74 Co-Authors with 154 Joint Publications 2,397 Co-Co-Authors all top 5 Co-Authors 101 single-authored 43 Tao, Youshan 22 Fila, Marek 10 Yanagida, Eiji 9 Wang, Yulan 8 Bellomo, Nicola 8 Lankeit, Johannes 8 Xiang, Zhaoyin 7 Stinner, Christian 5 King, John Robert 5 Painter, Kevin J. 5 Tello, José Ignacio 5 Yokota, Tomomi 4 Hillen, Thomas 4 Li, Genglin 4 Souplet, Philippe 4 Surulescu, Christina 4 Vazquez, Juan Luis 4 Wrzosek, Dariusz M. 3 Cieślak, Tomasz 3 Fujie, Kentaro 3 Lou, Yuan 2 Brunovský, Pavol 2 Černý, Aleš 2 Heinz, Stefan 2 Jüngel, Ansgar 2 Koch, Thorsten 2 Rodriguez, Nancy Y. 2 Stein, Oliver T. 2 Turner, Mark G. 2 Wang, Zhian 1 Ahn, Jaewook 1 Bai, Xueli 1 Bellouquid, Abdelghani 1 Berthold, Timo 1 Black, Tobias 1 Cao, Xinru 1 Chmiela, Antonia 1 Colasuonno, Francesca 1 Cosner, Chris 1 Desvillettes, Laurent 1 Deutsch, Andreas 1 Ding, Mengyao 1 Djie, Kianhwa C. 1 Dreyer, Wolfgang 1 Espejo, Elio E. 1 Evje, Steinar 1 Fuest, Mario 1 Fuhrmann, Jan 1 Gamrath, Gerald 1 Horstmann, Dirk 1 Huth, Robert 1 Ito, Akio 1 Kang, Kyungkeun 1 Kavallaris, Nikos Ioannis 1 King, Belinda Batten 1 Krzyżanowski, Piotr 1 Laurençot, Philippe 1 Lee, Jihoon 1 Li, Tong 1 Mielke, Alexander 1 Nikolić, Vanja 1 Outada, Nisrine 1 Quittner, Pavol 1 Rehberg, Joachim 1 Serrano, Felipe 1 Shinano, Yuji 1 Soler, Juan S. 1 Stevens, Angela 1 Suen, Anthony 1 Taskinen, Jari 1 Trescases, Ariane 1 Velázquez, Juan J. L. 1 Vigerske, Stefan 1 Xue, Chuan all top 5 Serials 22 Journal of Differential Equations 15 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 11 Nonlinearity 11 SIAM Journal on Mathematical Analysis 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Mathematical Methods in the Applied Sciences 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Communications in Partial Differential Equations 7 Discrete and Continuous Dynamical Systems 6 European Journal of Applied Mathematics 6 Advances in Differential Equations 6 Nonlinear Analysis. Real World Applications 5 Journal of Mathematical Analysis and Applications 5 Indiana University Mathematics Journal 5 Mathematische Annalen 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Journal of Dynamics and Differential Equations 5 NoDEA. 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Open Journal of Mathematical Optimization all top 5 Fields 243 Partial differential equations (35-XX) 169 Biology and other natural sciences (92-XX) 12 Fluid mechanics (76-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Mechanics of deformable solids (74-XX) 3 Operations research, mathematical programming (90-XX) 2 Ordinary differential equations (34-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Computer science (68-XX) 1 Real functions (26-XX) 1 Numerical analysis (65-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 230 Publications have been cited 13,152 times in 2,209 Documents Cited by ▼ Year ▼ Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model. Zbl 1190.92004 Winkler, Michael 771 2010 Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Zbl 1326.35397 Bellomo, N.; Bellouquid, A.; Tao, Y.; Winkler, M. 645 2015 Boundedness vs. blow-up in a chemotaxis system. Zbl 1085.35065 Horstmann, Dirk; Winkler, Michael 618 2005 Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. Zbl 1326.35053 Winkler, Michael 606 2013 Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity. Zbl 1382.35127 Tao, Youshan; Winkler, Michael 499 2012 Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source. Zbl 1290.35139 Winkler, Michael 491 2010 Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Zbl 1236.35192 Winkler, Michael 403 2012 A chemotaxis system with logistic source. Zbl 1121.37068 Tello, J. Ignacio; Winkler, Michael 393 2007 Stabilization in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1293.35220 Winkler, Michael 285 2014 Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Zbl 1351.35239 Winkler, Michael 230 2016 Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant. Zbl 1268.35016 Tao, Youshan; Winkler, Michael 228 2012 Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction. Zbl 1241.35028 Winkler, Michael 222 2011 Does a volume-filling effect always prevent chemotactic collapse? Zbl 1182.35220 Winkler, Michael 220 2010 Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Zbl 1345.35117 Bai, Xueli; Winkler, Michael 213 2016 Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening. Zbl 1293.35048 Winkler, Michael 209 2014 Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity. Zbl 1333.35104 Winkler, Michael 182 2015 Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion. Zbl 1301.35189 Stinner, Christian; Surulescu, Christina; Winkler, Michael 180 2014 Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect. Zbl 1183.92012 Winkler, Michael; Djie, Kianhwa C. 177 2010 How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Zbl 1356.35071 Winkler, Michael 177 2017 Finite-time blow-up in a quasilinear system of chemotaxis. Zbl 1136.92006 Cieślak, Tomasz; Winkler, Michael 172 2008 Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Zbl 1283.35154 Tao, Youshan; Winkler, Michael 170 2013 Chemotaxis with logistic source: very weak global solutions and their boundedness properties. Zbl 1147.92005 Winkler, Michael 165 2008 A chemotaxis-haptotaxis model: the roles of nonlinear diffusion and logistic source. Zbl 1259.35210 Tao, Youshan; Winkler, Michael 156 2011 How far can chemotactic cross-diffusion enforce exceeding carrying capacities? Zbl 1311.35040 Winkler, Michael 154 2014 Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Zbl 1328.35084 Tao, Youshan; Winkler, Michael 152 2015 Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Zbl 1276.35105 Tao, Youshan; Winkler, Michael 148 2012 Global solutions in a fully parabolic chemotaxis system with singular sensitivity. Zbl 1291.92018 Winkler, Michael 142 2011 Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048 Winkler, Michael 137 2018 Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion. Zbl 1328.35103 Tao, Youshan; Winkler, Michael 132 2015 Stabilization in a two-species chemotaxis system with a logistic source. Zbl 1260.92014 Tello, J. I.; Winkler, M. 125 2012 Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity. Zbl 1205.35037 Winkler, Michael 125 2010 A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. Zbl 1408.35132 Winkler, Michael 123 2019 Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities. Zbl 1330.35202 Winkler, Michael 122 2015 Competitive exclusion in a two-species chemotaxis model. Zbl 1319.92050 Stinner, C.; Tello, J. I.; Winkler, M. 118 2014 Energy-type estimates and global solvability in a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant. Zbl 1295.35144 Tao, Youshan; Winkler, Michael 116 2014 Stabilization in a chemotaxis model for tumor invasion. Zbl 1322.35059 Yokota, Tomomi; Winkler, Michael; Ito, Akio; Fujie, Kentarou 115 2016 Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Zbl 1356.35054 Tao, Youshan; Winkler, Michael 109 2016 Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068 Tao, Youshan; Winkler, Michael 94 2017 A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data. Zbl 1373.35166 Lankeit, Johannes; Winkler, Michael 90 2017 Global weak solutions in a chemotaxis system with large singular sensitivity. Zbl 1268.35072 Stinner, Christian; Winkler, Michael 88 2011 Convergence of a cancer invasion model to a logistic chemotaxis model. Zbl 1263.35204 Hillen, Thomas; Painter, Kevin J.; Winkler, Michael 88 2013 Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 1516.35092 Tao, Youshan; Winkler, Michael 87 2017 Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 86 2018 The two-dimensional Keller-Segel system with singular sensitivity and signal absorption: global large-data solutions and their relaxation properties. Zbl 1383.35099 Winkler, Michael 85 2016 A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240 Winkler, Michael 82 2018 A fourth-order parabolic equation modeling epitaxial thin film growth. Zbl 1029.35110 King, Belinda B.; Stein, Oliver; Winkler, Michael 78 2003 Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals. Zbl 1329.35075 Winkler, Michael; Tao, Youshan 78 2015 Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms. Zbl 1322.35054 Li, Tong; Suen, Anthony; Winkler, Michael; Xue, Chuan 74 2015 Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Zbl 1395.35038 Winkler, Michael 68 2018 A critical exponent in a degenerate parabolic equation. Zbl 1007.35043 Winkler, Michael 67 2002 Dominance of chemotaxis in a chemotaxis-haptotaxis model. Zbl 1293.35047 Tao, Youshan; Winkler, Michael 65 2014 A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166 Bellomo, Nicola; Winkler, Michael 65 2017 Blow-up prevention by logistic sources in a parabolic-elliptic Keller-Segel system with singular sensitivity. Zbl 1297.35051 Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi 63 2014 Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model. Zbl 1312.35171 Tao, Youshan; Winkler, Michael 62 2014 Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity. Zbl 1329.35011 Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi 61 2015 Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems. Zbl 1377.35158 Winkler, Michael 61 2017 Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044 Bellomo, Nicola; Winkler, Michael 61 2017 Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation. Zbl 1370.35059 Winkler, Michael 57 2017 Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations. Zbl 1441.35079 Winkler, Michael 57 2020 Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. Zbl 1428.35615 Bellomo, Nicola; Painter, Kevin J.; Tao, Youshan; Winkler, Michael 54 2019 Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity? Zbl 1409.35047 Winkler, Michael 52 2018 Persistence of mass in a chemotaxis system with logistic source. Zbl 1321.35084 Tao, Youshan; Winkler, Michael 51 2015 Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption. Zbl 1378.35165 Winkler, Michael 51 2018 Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Zbl 1404.35464 Winkler, Michael 50 2018 The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in \(L^{1}\). Zbl 1419.35099 Winkler, Michael 50 2020 Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization. Zbl 1392.35042 Espejo, Elio; Winkler, Michael 48 2018 Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems? Zbl 1483.35294 Winkler, Michael 46 2021 Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052 Winkler, Michael 43 2019 Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. Zbl 1497.35039 Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M. 42 2022 Facing low regularity in chemotaxis systems. Zbl 1436.92004 Lankeit, Johannes; Winkler, Michael 42 2020 The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1397.35322 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 40 2018 Stabilization in the logarithmic Keller-Segel system. Zbl 1391.35066 Winkler, Michael; Yokota, Tomomi 37 2018 Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food. Zbl 1425.35200 Tao, Youshan; Winkler, Michael 37 2019 Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065 Winkler, Michael 37 2020 Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132 Tao, Youshan; Winkler, Michael 37 2020 Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612 Winkler, Michael 36 2019 Global regularity versus infinite-time singularity formation in a chemotaxis model with volume-filling effect and degenerate diffusion. Zbl 1277.35223 Wang, Zhi-An; Winkler, Michael; Wrzosek, Dariusz 33 2012 Global existence and uniform boundedness of smooth solutions to a cross-diffusion system with equal diffusion rates. Zbl 1332.35172 Lou, Yuan; Winkler, Michael 32 2015 Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity. Zbl 1382.35048 Winkler, Michael 32 2017 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140 Souplet, Philippe; Winkler, Michael 31 2019 A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480 Tao, Youshan; Winkler, Michael 31 2020 Singular structure formation in a degenerate haptotaxis model involving myopic diffusion. Zbl 1391.35065 Winkler, Michael 29 2018 Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Zbl 1428.35611 Winkler, Michael 28 2019 Global bounded solutions in a two-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1364.35124 Cieślak, Tomasz; Winkler, Michael 27 2017 Global solvability in a three-dimensional Keller-Segel-Stokes system involving arbitrary superlinear logistic degradation. Zbl 1466.92020 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 27 2021 Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary. Zbl 1470.92044 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 27 2021 Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1367.35033 Cieślak, Tomasz; Winkler, Michael 26 2017 How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases. Zbl 1416.35049 Winkler, Michael 24 2019 Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation. Zbl 1460.35358 Winkler, Michael 24 2021 The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 23 2019 Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. Zbl 1295.35098 Lou, Yuan; Tao, Youshan; Winkler, Michael 22 2014 Global solutions in higher dimensions to a fourth-order parabolic equation modeling epitaxial thin-film growth. Zbl 1258.35192 Winkler, Michael 22 2011 Convergence rate for a parabolic equation with supercritical nonlinearity. Zbl 1087.35049 Fila, Marek; Winkler, Michael; Yanagida, Eiji 21 2005 Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250 Li, Genglin; Tao, Youshan; Winkler, Michael 21 2020 A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181 Tao, Youshan; Winkler, Michael 21 2019 Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. Zbl 1466.35060 Winkler, Michael 21 2021 Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Zbl 1458.35076 Tao, Youshan; Winkler, Michael 21 2021 Singularity formation in chemotaxis systems with volume-filling effect. Zbl 1255.35213 Wang, Zhi-An; Winkler, Michael; Wrzosek, Dariusz 20 2011 Grow up rate of solutions for a supercritical semilinear diffusion equation. Zbl 1072.35042 Fila, Marek; Winkler, Michael; Yanagida, Eiji 20 2004 A fully cross-diffusive two-component evolution system: existence and qualitative analysis via entropy-consistent thin-film-type approximation. Zbl 1471.35278 Tao, Youshan; Winkler, Michael 20 2021 Approaching critical decay in a strongly degenerate parabolic equation. Zbl 07818483 Winkler, Michael 1 2024 \(L^1\) solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation. Zbl 1517.35096 Winkler, Michael 19 2023 Does Leray’s structure theorem withstand buoyancy-driven chemotaxis-fluid interaction? Zbl 1520.35027 Winkler, Michael 13 2023 Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Zbl 1518.35109 Li, Genglin; Winkler, Michael 11 2023 Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. Zbl 1501.35057 Desvillettes, Laurent; Laurençot, Philippe; Trescases, Ariane; Winkler, Michael 10 2023 Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Zbl 1505.35340 Tao, Youshan; Winkler, Michael 8 2023 Application of the Moser-Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. Zbl 07735866 Winkler, Michael 7 2023 Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration-consumption interaction. Zbl 1504.35181 Winkler, Michael 6 2023 Finite-time blow-up in a repulsive chemotaxis-consumption system. Zbl 1518.35155 Wang, Yulan; Winkler, Michael 4 2023 Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Zbl 1525.35038 Tao, Youshan; Winkler, Michael 3 2023 A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. Zbl 1521.35053 Ahn, Jaewook; Winkler, Michael 2 2023 Adaptive cut selection in mixed-integer linear programming. Zbl 1522.90045 Turner, Mark; Koch, Thorsten; Serrano, Felipe; Winkler, Michael 2 2023 Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration-consumption interaction. Zbl 1525.35040 Winkler, Michael 2 2023 Classical solutions to Cauchy problems for parabolic-elliptic systems of Keller-Segel type. Zbl 1523.35268 Winkler, Michael 2 2023 Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Zbl 1518.35439 Tao, Youshan; Winkler, Michael 1 2023 Exponential grow-up rates in a quasilinear Keller-Segel system. Zbl 1509.35325 Winkler, Michael 1 2023 A result on parabolic gradient regularity in Orlicz spaces and application to absorption-induced blow-up prevention in a Keller-Segel-type cross-diffusion system. Zbl 07794925 Winkler, Michael 1 2023 Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. Zbl 1497.35039 Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M. 42 2022 Reaction-driven relaxation in three-dimensional Keller-Segel-Navier-Stokes interaction. Zbl 1486.35102 Winkler, Michael 18 2022 Unlimited growth in logarithmic Keller-Segel systems. Zbl 1480.35383 Winkler, Michael 15 2022 Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system. Zbl 1496.35228 Tao, Youshan; Winkler, Michael 14 2022 A critical blow-up exponent for flux limiation in a Keller-Segel system. Zbl 1501.35094 Winkler, Michael 13 2022 Global mass-preserving solutions to a chemotaxis-fluid model involving Dirichlet boundary conditions for the signal. Zbl 1484.92013 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 10 2022 Chemotaxis-Stokes interaction with very weak diffusion enhancement: blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings. Zbl 1511.35053 Winkler, Michael 10 2022 A family of mass-critical Keller-Segel systems. Zbl 1522.35524 Winkler, Michael 8 2022 Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy. Zbl 1484.35363 Tao, Youshan; Winkler, Michael 8 2022 On the global existence and qualitative behaviour of one-dimensional solutions to a model for urban crime. Zbl 1503.35234 Rodriguez, Nancy; Winkler, Michael 7 2022 Global weak solutions and absorbing sets in a chemotaxis-Navier-Stokes system with prescribed signal concentration on the boundary. Zbl 1487.35372 Black, Tobias; Winkler, Michael 7 2022 A unifying approach toward boundedness in Keller-Segel type cross-diffusion systems via conditional \(L^{\infty}\) estimates for taxis gradients. Zbl 1525.35050 Winkler, Michael 6 2022 Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary. Zbl 1481.35023 Lankeit, Johannes; Winkler, Michael 5 2022 Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities. Zbl 1503.35051 Winkler, Michael 5 2022 Nonnegative solutions to a doubly degenerate nutrient taxis system. Zbl 1483.35127 Li, Genglin; Winkler, Michael 5 2022 A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system. Zbl 1494.35047 Fuhrmann, Jan; Lankeit, Johannes; Winkler, Michael 4 2022 Global weak solutions to a chemotaxis-Navier-Stokes system in \(\mathbb{R}^3 \). Zbl 1498.92032 Kang, Kyungkeun; Lee, Jihoon; Winkler, Michael 4 2022 Small-signal solutions of a two-dimensional doubly degenerate taxis system modeling bacterial motion in nutrient-poor environments. Zbl 1479.35224 Winkler, Michael 3 2022 A smallness condition ensuring boundedness in a two-dimensional chemotaxis-Navier-Stokes system involving Dirichlet boundary conditions for the signal. Zbl 1491.92033 Wang, Yu Lan; Winkler, Michael; Xiang, Zhao Yin 3 2022 Taxis-driven persistent localization in a degenerate Keller-Segel system. Zbl 1505.35045 Stevens, Angela; Winkler, Michael 1 2022 Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects. Zbl 1485.35266 Lankeit, Johannes; Winkler, Michael 1 2022 Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems? Zbl 1483.35294 Winkler, Michael 46 2021 Global solvability in a three-dimensional Keller-Segel-Stokes system involving arbitrary superlinear logistic degradation. Zbl 1466.92020 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 27 2021 Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary. Zbl 1470.92044 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 27 2021 Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation. Zbl 1460.35358 Winkler, Michael 24 2021 Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. Zbl 1466.35060 Winkler, Michael 21 2021 Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Zbl 1458.35076 Tao, Youshan; Winkler, Michael 21 2021 A fully cross-diffusive two-component evolution system: existence and qualitative analysis via entropy-consistent thin-film-type approximation. Zbl 1471.35278 Tao, Youshan; Winkler, Michael 20 2021 Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. Zbl 1479.35120 Tao, Youshan; Winkler, Michael 18 2021 Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation. Zbl 1468.35220 Winkler, Michael 17 2021 Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity. Zbl 1453.35115 Winkler, Michael 14 2021 Taxis-driven formation of singular hotspots in a May-Nowak-type model for virus infection. Zbl 1461.35201 Tao, Youshan; Winkler, Michael 13 2021 A critical virus production rate for efficiency of oncolytic virotherapy. Zbl 1526.92012 Tao, Youshan; Winkler, Michael 12 2021 Does spatial homogeneity ultimately prevail in nutrient taxis systems? A paradigm for structure support by rapid diffusion decay in an autonomous parabolic flow. Zbl 1455.35026 Winkler, Michael 8 2021 Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption. Zbl 1464.35051 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 8 2021 Small-density solutions in Keller-Segel systems involving rapidly decaying diffusivities. Zbl 1471.35064 Ding, Mengyao; Winkler, Michael 8 2021 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). Zbl 1503.35243 Surulescu, Christina; Winkler, Michael 3 2021 The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. Zbl 1465.35378 Tao, Youshan; Winkler, Michael 1 2021 Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations. Zbl 1441.35079 Winkler, Michael 57 2020 The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in \(L^{1}\). Zbl 1419.35099 Winkler, Michael 50 2020 Facing low regularity in chemotaxis systems. Zbl 1436.92004 Lankeit, Johannes; Winkler, Michael 42 2020 Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065 Winkler, Michael 37 2020 Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132 Tao, Youshan; Winkler, Michael 37 2020 A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480 Tao, Youshan; Winkler, Michael 31 2020 Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250 Li, Genglin; Tao, Youshan; Winkler, Michael 21 2020 Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system. Zbl 1459.92019 Winkler, Michael 18 2020 Can simultaneous density-determined enhancement of diffusion and cross-diffusion foster boundedness in Keller-Segel type systems involving signal-dependent motilities? Zbl 1454.35224 Winkler, Michael 17 2020 Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation. Zbl 1451.35226 Rodríguez, Nancy; Winkler, Michael 15 2020 Mathematical analysis of two competing cancer cell migration mechanisms driven by interstitial fluid flow. Zbl 1442.35469 Evje, Steinar; Winkler, Michael 8 2020 Single-point blow-up in the Cauchy problem for the higher-dimensional Keller-Segel system. Zbl 1452.35227 Winkler, Michael 7 2020 Boundedness in a two-dimensional Keller-Segel-Navier-Stokes system involving a rapidly diffusing repulsive signal. Zbl 1432.92021 Winkler, Michael 6 2020 Chemotaxis systems in complex frameworks: pattern formation, qualitative analysis and blowup prevention. Zbl 1451.92062 Bellomo, N.; Tao, Y.; Winkler, M. 5 2020 Refined regularity and stabilization properties in a degenerate haptotaxis system. Zbl 1437.35434 Winkler, Michael; Stinner, Christian 4 2020 Can fluid interaction influence the critical mass for taxis-driven blow-up in bounded planar domains? Zbl 1464.35046 Winkler, Michael 3 2020 A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. Zbl 1408.35132 Winkler, Michael 123 2019 Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. Zbl 1428.35615 Bellomo, Nicola; Painter, Kevin J.; Tao, Youshan; Winkler, Michael 54 2019 Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052 Winkler, Michael 43 2019 Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food. Zbl 1425.35200 Tao, Youshan; Winkler, Michael 37 2019 Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612 Winkler, Michael 36 2019 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140 Souplet, Philippe; Winkler, Michael 31 2019 Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Zbl 1428.35611 Winkler, Michael 28 2019 How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases. Zbl 1416.35049 Winkler, Michael 24 2019 The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 23 2019 A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181 Tao, Youshan; Winkler, Michael 21 2019 Boundedness in a chemotaxis-May-Nowak model for virus dynamics with mildly saturated chemotactic sensitivity. Zbl 1423.35172 Winkler, Michael 19 2019 Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension. Zbl 1411.35146 Tao, Youshan; Winkler, Michael 19 2019 How strong singularities can be regularized by logistic degradation in the Keller-Segel system? Zbl 1437.35004 Winkler, Michael 15 2019 Does repulsion-type directional preference in chemotactic migration continue to regularize Keller-Segel systems when coupled to the Navier-Stokes equations? Zbl 1429.92042 Winkler, Michael 11 2019 Boundedness and stabilization in a population model with cross-diffusion for one species. Zbl 1439.35275 Tao, Youshan; Winkler, Michael 9 2019 A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation. Zbl 1428.26026 Fila, Marek; Winkler, Michael 6 2019 Structure-driven fix-and-propagate heuristics for mixed integer programming. Zbl 1432.90091 Gamrath, Gerald; Berthold, Timo; Heinz, Stefan; Winkler, Michael 5 2019 Instantaneous regularization of distributions from \((C^0)^\star \times L^2\) in the one-dimensional parabolic Keller-Segel system. Zbl 1428.35632 Winkler, Michael 5 2019 Migration-driven benefit in a two-species nutrient taxis system. Zbl 1425.92033 Krzyżanowski, Piotr; Winkler, Michael; Wrzosek, Dariusz 3 2019 Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal degenerate parabolic equation arising in game theory. Zbl 1433.35181 Lankeit, Johannes; Winkler, Michael 1 2019 Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048 Winkler, Michael 137 2018 Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 86 2018 A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240 Winkler, Michael 82 2018 Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Zbl 1395.35038 Winkler, Michael 68 2018 Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity? Zbl 1409.35047 Winkler, Michael 52 2018 Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption. Zbl 1378.35165 Winkler, Michael 51 2018 Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Zbl 1404.35464 Winkler, Michael 50 2018 Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization. Zbl 1392.35042 Espejo, Elio; Winkler, Michael 48 2018 The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1397.35322 Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 40 2018 ...and 130 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,788 Authors 181 Winkler, Michael 79 Mu, Chunlai 58 Tao, Youshan 53 Zheng, Jiashan 52 Zheng, Pan 42 Wang, Liangchen 40 Yokota, Tomomi 37 Liu, Bin 37 Wang, Zhian 36 Lankeit, Johannes 34 Zheng, Sining 33 Ren, Guoqiang 32 Wang, Yifu 29 Xiang, Zhaoyin 26 Jin, Haiyang 24 Shen, Wenxian 23 Kang, Kyungkeun 23 Lin, Ke 23 Viglialoro, Giuseppe 23 Xiang, Tian 22 Wang, Qi 21 Fujie, Kentaro 21 Wang, Wei 20 Fila, Marek 20 Liu, Ji 20 Mizukami, Masaaki 19 Liu, Zuhan 18 Negreanu, Mihaela 17 Hu, Xuegang 17 Liu, Changchun 17 Stinner, Christian 17 Wang, Yulan 16 Black, Tobias 16 Elaiw, Ahmed M. 16 Fuest, Mario 16 Jiang, Jie 16 Qiu, Shuyan 16 Surulescu, Christina 16 Yin, Jingxue 16 Zhou, Ling 15 Bellomo, Nicola 15 Cao, Xinru 15 Dai, Feng 15 Guo, Shangjiang 15 Jin, Chunhua 15 Tello, José Ignacio 15 Tu, Xinyu 15 Zhang, Qingshan 14 Guillén González, Francisco M. 14 Ke, Yuanyuan 14 Li, Zhongping 14 Yanagida, Eiji 14 Zhang, Qian 13 Painter, Kevin J. 13 Wang, Jianping 13 Wang, Yilong 13 Zhao, Jie 12 Hillen, Thomas 12 Ishida, Sachiko 12 Laurençot, Philippe 12 Lee, Jihoon 12 Li, Xie 12 Li, Yuxiang 11 Cieślak, Tomasz 11 Li, Dan 11 Pan, Xu 11 Rueda-Gómez, Diego Armando 11 Salako, Rachidi Bolaji 11 Shangerganesh, Lingeshwaran 11 Villamizar-Roa, Elder Jesús 11 Yoon, Changwook 10 Ahn, Jaewook 10 Chiyo, Yutaro 10 Fu, Shengmao 10 Li, Jing 10 Lyu, Wenbin 10 Morales-Rodrigo, Cristian 10 Souplet, Philippe 10 Zhou, Jun 9 Baghaei, Khadijeh 9 Ding, Mengyao 9 Li, Bin 9 Li, Yan 9 Liu, Zhengrong 9 Shi, Junping 9 Vargas, Antonio Manuel 9 Wang, Mingxin 9 Xie, Li 9 Zhao, Xiangdong 8 Alshamrani, Noura H. 8 Carrillo de la Plata, José Antonio 8 Frassu, Silvia 8 Lei, Yuzhu 8 Ma, Manjun 8 Marras, Monica 8 Rodríguez-Bellido, Maria Angeles 8 Suárez, Antonio 8 Tanaka, Yuya 8 Tao, Xueyan 8 Vernier-Piro, Stella ...and 1,688 more Authors all top 5 Cited in 235 Serials 226 Journal of Differential Equations 176 Journal of Mathematical Analysis and Applications 127 Discrete and Continuous Dynamical Systems. 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Mathematics 5 Evolution Equations and Control Theory 5 Journal of Elliptic and Parabolic Equations 5 SN Partial Differential Equations and Applications 4 Communications in Mathematical Physics 4 Computer Methods in Applied Mechanics and Engineering 4 Physica A 4 Chaos, Solitons and Fractals 4 Indiana University Mathematics Journal 4 Journal of Computational and Applied Mathematics 4 Japan Journal of Industrial and Applied Mathematics 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Journal of Inequalities and Applications 4 Journal of Dynamical and Control Systems 4 SIAM Journal on Applied Dynamical Systems 4 Analysis and Applications (Singapore) 4 Open Mathematics 4 Mathematics in Engineering 3 Journal d’Analyse Mathématique 3 Archiv der Mathematik 3 Bulletin of the London Mathematical Society 3 Czechoslovak Mathematical Journal 3 Monatshefte für Mathematik 3 SIAM Journal on Numerical Analysis 3 Acta Mathematicae Applicatae Sinica. 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