Edit Profile (opens in new tab) Winkler, Michael Compute Distance To: Compute 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: 222 Publications since 2001 2 Contributions as Editor Co-Authors: 66 Co-Authors with 136 Joint Publications 2,071 Co-Co-Authors all top 5 Co-Authors 88 single-authored 38 Tao, Youshan 22 Fila, Marek 10 Yanagida, Eiji 8 Wang, Yulan 8 Xiang, Zhaoyin 7 Bellomo, Nicola 7 Lankeit, Johannes 7 Stinner, Christian 5 King, John Robert 5 Tello, José Ignacio 4 Hillen, Thomas 4 Painter, Kevin J. 4 Souplet, Philippe 4 Surulescu, Christina 4 Vazquez, Juan Luis 4 Wrzosek, Dariusz M. 4 Yokota, Tomomi 3 Cieślak, Tomasz 3 Fujie, Kentaro 3 Lou, Yuan 2 Brunovský, Pavol 2 Černý, Aleš 2 Heinz, Stefan 2 Jüngel, Ansgar 2 Li, Genglin 2 Rodriguez, Nancy Y. 2 Stein, Oliver T. 2 Wang, Zhian 1 Bai, Xueli 1 Bellouquid, Abdelghani 1 Berthold, Timo 1 Black, Tobias 1 Cao, Xinru 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 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 Outada, Nisrine 1 Quittner, Pavol 1 Rehberg, Joachim 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 21 Journal of Differential Equations 13 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 11 SIAM Journal on Mathematical Analysis 10 Nonlinearity 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Communications in Partial Differential Equations 7 Mathematical Methods in the Applied Sciences 7 Discrete and Continuous Dynamical Systems 6 European Journal of Applied Mathematics 5 Journal of Mathematical Analysis and Applications 5 Indiana University Mathematics Journal 5 Mathematische Annalen 5 NoDEA. Nonlinear Differential Equations and Applications 5 Advances in Differential Equations 5 Nonlinear Analysis. Real World Applications 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Journal of Dynamics and Differential Equations 4 Journal of Evolution Equations 4 Discrete and Continuous Dynamical Systems. 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Series B 1 SN Partial Differential Equations and Applications all top 5 Fields 218 Partial differential equations (35-XX) 150 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 Dynamical systems and ergodic theory (37-XX) 3 Mechanics of deformable solids (74-XX) 2 General and overarching topics; collections (00-XX) 2 Ordinary differential equations (34-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Operations research, mathematical programming (90-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 206 Publications have been cited 10,472 times in 1,809 Documents Cited by ▼ Year ▼ Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model. Zbl 1190.92004Winkler, Michael 617 2010 Boundedness vs. blow-up in a chemotaxis system. Zbl 1085.35065Horstmann, Dirk; Winkler, Michael 527 2005 Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Zbl 1326.35397Bellomo, N.; Bellouquid, A.; Tao, Y.; Winkler, M. 521 2015 Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. Zbl 1326.35053Winkler, Michael 496 2013 Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity. Zbl 1382.35127Tao, Youshan; Winkler, Michael 416 2012 Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source. Zbl 1290.35139Winkler, Michael 413 2010 A chemotaxis system with logistic source. Zbl 1121.37068Tello, J. Ignacio; Winkler, Michael 334 2007 Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Zbl 1236.35192Winkler, Michael 328 2012 Stabilization in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1293.35220Winkler, Michael 228 2014 Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction. Zbl 1241.35028Winkler, Michael 191 2011 Does a volume-filling effect always prevent chemotactic collapse? Zbl 1182.35220Winkler, Michael 189 2010 Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening. Zbl 1293.35048Winkler, Michael 186 2014 Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant. Zbl 1268.35016Tao, Youshan; Winkler, Michael 185 2012 Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Zbl 1351.35239Winkler, Michael 183 2016 Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Zbl 1345.35117Bai, Xueli; Winkler, Michael 169 2016 Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect. Zbl 1183.92012Winkler, Michael; Djie, Kianhwa C. 157 2010 Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity. Zbl 1333.35104Winkler, Michael 152 2015 Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Zbl 1283.35154Tao, Youshan; Winkler, Michael 150 2013 Finite-time blow-up in a quasilinear system of chemotaxis. Zbl 1136.92006Cieślak, Tomasz; Winkler, Michael 148 2008 Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion. Zbl 1301.35189Stinner, Christian; Surulescu, Christina; Winkler, Michael 147 2014 Chemotaxis with logistic source: very weak global solutions and their boundedness properties. Zbl 1147.92005Winkler, Michael 141 2008 How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Zbl 1356.35071Winkler, Michael 135 2017 A chemotaxis-haptotaxis model: the roles of nonlinear diffusion and logistic source. Zbl 1259.35210Tao, Youshan; Winkler, Michael 135 2011 How far can chemotactic cross-diffusion enforce exceeding carrying capacities? Zbl 1311.35040Winkler, Michael 133 2014 Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Zbl 1328.35084Tao, Youshan; Winkler, Michael 130 2015 Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Zbl 1276.35105Tao, Youshan; Winkler, Michael 130 2012 Global solutions in a fully parabolic chemotaxis system with singular sensitivity. Zbl 1291.92018Winkler, Michael 116 2011 Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity. Zbl 1205.35037Winkler, Michael 115 2010 Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion. Zbl 1328.35103Tao, Youshan; Winkler, Michael 113 2015 Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048Winkler, Michael 108 2018 Stabilization in a two-species chemotaxis system with a logistic source. Zbl 1260.92014Tello, J. I.; Winkler, M. 107 2012 Competitive exclusion in a two-species chemotaxis model. Zbl 1319.92050Stinner, C.; Tello, J. I.; Winkler, M. 104 2014 A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. Zbl 1408.35132Winkler, Michael 92 2019 Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities. Zbl 1330.35202Winkler, Michael 89 2015 Energy-type estimates and global solvability in a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant. Zbl 1295.35144Tao, Youshan; Winkler, Michael 89 2014 Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Zbl 1356.35054Tao, Youshan; Winkler, Michael 89 2016 Stabilization in a chemotaxis model for tumor invasion. Zbl 1322.35059Yokota, Tomomi; Winkler, Michael; Ito, Akio; Fujie, Kentarou 89 2016 Convergence of a cancer invasion model to a logistic chemotaxis model. Zbl 1263.35204Hillen, Thomas; Painter, Kevin J.; Winkler, Michael 79 2013 Global weak solutions in a chemotaxis system with large singular sensitivity. Zbl 1268.35072Stinner, Christian; Winkler, Michael 76 2011 Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068Tao, Youshan; Winkler, Michael 72 2017 Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 71 2018 A fourth-order parabolic equation modeling epitaxial thin film growth. Zbl 1029.35110King, Belinda B.; Stein, Oliver; Winkler, Michael 68 2003 A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data. Zbl 1373.35166Lankeit, Johannes; Winkler, Michael 68 2017 Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals. Zbl 1329.35075Winkler, Michael; Tao, Youshan 67 2015 A critical exponent in a degenerate parabolic equation. Zbl 1007.35043Winkler, Michael 64 2002 Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms. Zbl 1322.35054Li, Tong; Suen, Anthony; Winkler, Michael; Xue, Chuan 63 2015 Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 06761738Tao, Youshan; Winkler, Michael 63 2017 A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240Winkler, Michael 61 2018 The two-dimensional Keller-Segel system with singular sensitivity and signal absorption: global large-data solutions and their relaxation properties. Zbl 1383.35099Winkler, Michael 56 2016 Dominance of chemotaxis in a chemotaxis-haptotaxis model. Zbl 1293.35047Tao, Youshan; Winkler, Michael 56 2014 Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model. Zbl 1312.35171Tao, Youshan; Winkler, Michael 55 2014 Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Zbl 1395.35038Winkler, Michael 55 2018 Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems. Zbl 1377.35158Winkler, Michael 51 2017 Blow-up prevention by logistic sources in a parabolic-elliptic Keller-Segel system with singular sensitivity. Zbl 1297.35051Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi 50 2014 A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166Bellomo, Nicola; Winkler, Michael 49 2017 Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044Bellomo, Nicola; Winkler, Michael 48 2017 Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity. Zbl 1329.35011Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi 47 2015 Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity? Zbl 1409.35047Winkler, Michael 43 2018 Persistence of mass in a chemotaxis system with logistic source. Zbl 1321.35084Tao, Youshan; Winkler, Michael 42 2015 Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation. Zbl 1370.35059Winkler, Michael 41 2017 Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization. Zbl 1392.35042Espejo, Elio; Winkler, Michael 37 2018 Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. Zbl 1428.35615Bellomo, Nicola; Painter, Kevin J.; Tao, Youshan; Winkler, Michael 35 2019 The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1397.35322Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 34 2018 Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052Winkler, Michael 33 2019 Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption. Zbl 1378.35165Winkler, Michael 33 2018 Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Zbl 1404.35464Winkler, Michael 32 2018 The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in \(L^{1}\). Zbl 1419.35099Winkler, Michael 32 2020 Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food. Zbl 1425.35200Tao, Youshan; Winkler, Michael 30 2019 Global regularity versus infinite-time singularity formation in a chemotaxis model with volume-filling effect and degenerate diffusion. Zbl 1277.35223Wang, Zhi-An; Winkler, Michael; Wrzosek, Dariusz 30 2012 Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations. Zbl 1441.35079Winkler, Michael 30 2020 Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612Winkler, Michael 29 2019 Global existence and uniform boundedness of smooth solutions to a cross-diffusion system with equal diffusion rates. Zbl 1332.35172Lou, Yuan; Winkler, Michael 28 2015 Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity. Zbl 1382.35048Winkler, Michael 26 2017 Facing low regularity in chemotaxis systems. Zbl 1436.92004Lankeit, Johannes; Winkler, Michael 25 2020 Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132Tao, Youshan; Winkler, Michael 25 2020 Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065Winkler, Michael 25 2020 Global bounded solutions in a two-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1364.35124Cieślak, Tomasz; Winkler, Michael 24 2017 Stabilization in the logarithmic Keller-Segel system. Zbl 1391.35066Winkler, Michael; Yokota, Tomomi 24 2018 A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480Tao, Youshan; Winkler, Michael 24 2020 Singular structure formation in a degenerate haptotaxis model involving myopic diffusion. Zbl 1391.35065Winkler, Michael 23 2018 Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1367.35033Cieślak, Tomasz; Winkler, Michael 22 2017 Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems? Zbl 1483.35294Winkler, Michael 21 2021 Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. Zbl 1295.35098Lou, Yuan; Tao, Youshan; Winkler, Michael 21 2014 Global solutions in higher dimensions to a fourth-order parabolic equation modeling epitaxial thin-film growth. Zbl 1258.35192Winkler, Michael 21 2011 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140Souplet, Philippe; Winkler, Michael 20 2019 Convergence rate for a parabolic equation with supercritical nonlinearity. Zbl 1087.35049Fila, Marek; Winkler, Michael; Yanagida, Eiji 20 2005 Grow up rate of solutions for a supercritical semilinear diffusion equation. Zbl 1072.35042Fila, Marek; Winkler, Michael; Yanagida, Eiji 19 2004 A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181Tao, Youshan; Winkler, Michael 19 2019 Optimal lower bound of the grow-up rate for a supercritical parabolic equation. Zbl 1102.35017Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji 18 2006 Singularity formation in chemotaxis systems with volume-filling effect. Zbl 1255.35213Wang, Zhi-An; Winkler, Michael; Wrzosek, Dariusz 18 2011 Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027Quittner, Pavol; Souplet, Philippe; Winkler, Michael 17 2004 Rate of convergence to Barenblatt profiles for the fast diffusion equation. Zbl 1315.76032Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji 17 2012 How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases. Zbl 1416.35049Winkler, Michael 17 2019 Global solvability in a three-dimensional Keller-Segel-Stokes system involving arbitrary superlinear logistic degradation. Zbl 1466.92020Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 17 2021 Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Zbl 1428.35611Winkler, Michael 17 2019 The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 16 2019 Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension. Zbl 1411.35146Tao, Youshan; Winkler, Michael 16 2019 Amorphous molecular beam epitaxy: global solutions and absorbing sets. Zbl 1120.35045Stein, O.; Winkler, M. 16 2005 Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary. Zbl 1470.92044Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 15 2021 Global weak solutions to a strongly degenerate haptotaxis model. Zbl 1390.35164Winkler, Michael; Surulescu, Christina 14 2017 Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. Zbl 1501.35057Desvillettes, Laurent; Laurençot, Philippe; Trescases, Ariane; Winkler, Michael 2 2023 Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Zbl 1505.35340Tao, Youshan; Winkler, Michael 2 2023 Reaction-driven relaxation in three-dimensional Keller-Segel-Navier-Stokes interaction. Zbl 1486.35102Winkler, Michael 7 2022 Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system. Zbl 1496.35228Tao, Youshan; Winkler, Michael 6 2022 Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. Zbl 1497.35039Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M. 5 2022 Global mass-preserving solutions to a chemotaxis-fluid model involving Dirichlet boundary conditions for the signal. Zbl 1484.92013Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 4 2022 Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy. Zbl 1484.35363Tao, Youshan; Winkler, Michael 2 2022 Small-signal solutions of a two-dimensional doubly degenerate taxis system modeling bacterial motion in nutrient-poor environments. Zbl 1479.35224Winkler, Michael 2 2022 Unlimited growth in logarithmic Keller-Segel systems. Zbl 1480.35383Winkler, Michael 2 2022 A critical blow-up exponent for flux limiation in a Keller-Segel system. Zbl 1501.35094Winkler, Michael 2 2022 Global weak solutions and absorbing sets in a chemotaxis-Navier-Stokes system with prescribed signal concentration on the boundary. Zbl 1487.35372Black, Tobias; Winkler, Michael 1 2022 Nonnegative solutions to a doubly degenerate nutrient taxis system. Zbl 1483.35127Li, Genglin; Winkler, Michael 1 2022 Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary. Zbl 1481.35023Lankeit, Johannes; Winkler, Michael 1 2022 Global weak solutions to a chemotaxis-Navier-Stokes system in \(\mathbb{R}^3 \). Zbl 1498.92032Kang, Kyungkeun; Lee, Jihoon; Winkler, Michael 1 2022 Chemotaxis-Stokes interaction with very weak diffusion enhancement: blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings. Zbl 07661224Winkler, Michael 1 2022 Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems? Zbl 1483.35294Winkler, Michael 21 2021 Global solvability in a three-dimensional Keller-Segel-Stokes system involving arbitrary superlinear logistic degradation. Zbl 1466.92020Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 17 2021 Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary. Zbl 1470.92044Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 15 2021 Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. Zbl 1466.35060Winkler, Michael 13 2021 Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation. Zbl 1460.35358Winkler, Michael 13 2021 Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Zbl 1458.35076Tao, Youshan; Winkler, Michael 12 2021 A fully cross-diffusive two-component evolution system: existence and qualitative analysis via entropy-consistent thin-film-type approximation. Zbl 1471.35278Tao, Youshan; Winkler, Michael 12 2021 Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation. Zbl 1468.35220Winkler, Michael 9 2021 Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity. Zbl 1453.35115Winkler, Michael 8 2021 Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. Zbl 1479.35120Tao, Youshan; Winkler, Michael 6 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 1455.35026Winkler, Michael 5 2021 Small-density solutions in Keller-Segel systems involving rapidly decaying diffusivities. Zbl 1471.35064Ding, Mengyao; Winkler, Michael 5 2021 Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption. Zbl 1464.35051Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 4 2021 Taxis-driven formation of singular hotspots in a May-Nowak-type model for virus infection. Zbl 1461.35201Tao, Youshan; Winkler, Michael 3 2021 A critical virus production rate for efficiency of oncolytic virotherapy. Zbl 07629666Tao, Youshan; Winkler, Michael 3 2021 The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. Zbl 1465.35378Tao, Youshan; Winkler, Michael 1 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 1503.35243Surulescu, Christina; Winkler, Michael 1 2021 The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in \(L^{1}\). Zbl 1419.35099Winkler, Michael 32 2020 Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations. Zbl 1441.35079Winkler, Michael 30 2020 Facing low regularity in chemotaxis systems. Zbl 1436.92004Lankeit, Johannes; Winkler, Michael 25 2020 Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132Tao, Youshan; Winkler, Michael 25 2020 Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065Winkler, Michael 25 2020 A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480Tao, Youshan; Winkler, Michael 24 2020 Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250Li, Genglin; Tao, Youshan; Winkler, Michael 11 2020 Can simultaneous density-determined enhancement of diffusion and cross-diffusion foster boundedness in Keller-Segel type systems involving signal-dependent motilities? Zbl 1454.35224Winkler, Michael 9 2020 Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system. Zbl 1459.92019Winkler, Michael 8 2020 Mathematical analysis of two competing cancer cell migration mechanisms driven by interstitial fluid flow. Zbl 1442.35469Evje, Steinar; Winkler, Michael 6 2020 Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation. Zbl 1451.35226Rodríguez, Nancy; Winkler, Michael 5 2020 Chemotaxis systems in complex frameworks: pattern formation, qualitative analysis and blowup prevention. Zbl 1451.92062Bellomo, N.; Tao, Y.; Winkler, M. 3 2020 Single-point blow-up in the Cauchy problem for the higher-dimensional Keller-Segel system. Zbl 1452.35227Winkler, Michael 3 2020 Boundedness in a two-dimensional Keller-Segel-Navier-Stokes system involving a rapidly diffusing repulsive signal. Zbl 1432.92021Winkler, Michael 3 2020 Refined regularity and stabilization properties in a degenerate haptotaxis system. Zbl 1437.35434Winkler, Michael; Stinner, Christian 2 2020 A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. Zbl 1408.35132Winkler, Michael 92 2019 Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. Zbl 1428.35615Bellomo, Nicola; Painter, Kevin J.; Tao, Youshan; Winkler, Michael 35 2019 Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052Winkler, Michael 33 2019 Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food. Zbl 1425.35200Tao, Youshan; Winkler, Michael 30 2019 Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612Winkler, Michael 29 2019 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140Souplet, Philippe; Winkler, Michael 20 2019 A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181Tao, Youshan; Winkler, Michael 19 2019 How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases. Zbl 1416.35049Winkler, Michael 17 2019 Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Zbl 1428.35611Winkler, Michael 17 2019 The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 16 2019 Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension. Zbl 1411.35146Tao, Youshan; Winkler, Michael 16 2019 How strong singularities can be regularized by logistic degradation in the Keller-Segel system? Zbl 1437.35004Winkler, Michael 9 2019 Does repulsion-type directional preference in chemotactic migration continue to regularize Keller-Segel systems when coupled to the Navier-Stokes equations? Zbl 1429.92042Winkler, Michael 8 2019 Boundedness in a chemotaxis-May-Nowak model for virus dynamics with mildly saturated chemotactic sensitivity. Zbl 1423.35172Winkler, Michael 7 2019 Boundedness and stabilization in a population model with cross-diffusion for one species. Zbl 1439.35275Tao, Youshan; Winkler, Michael 7 2019 A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation. Zbl 1428.26026Fila, Marek; Winkler, Michael 4 2019 Structure-driven fix-and-propagate heuristics for mixed integer programming. Zbl 1432.90091Gamrath, Gerald; Berthold, Timo; Heinz, Stefan; Winkler, Michael 3 2019 Instantaneous regularization of distributions from \((C^0)^\star \times L^2\) in the one-dimensional parabolic Keller-Segel system. Zbl 1428.35632Winkler, Michael 3 2019 Migration-driven benefit in a two-species nutrient taxis system. Zbl 1425.92033Krzyżanowski, Piotr; Winkler, Michael; Wrzosek, Dariusz 2 2019 Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal degenerate parabolic equation arising in game theory. Zbl 1433.35181Lankeit, Johannes; Winkler, Michael 1 2019 Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048Winkler, Michael 108 2018 Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 71 2018 A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240Winkler, Michael 61 2018 Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Zbl 1395.35038Winkler, Michael 55 2018 Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity? Zbl 1409.35047Winkler, Michael 43 2018 Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization. Zbl 1392.35042Espejo, Elio; Winkler, Michael 37 2018 The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1397.35322Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin 34 2018 Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption. Zbl 1378.35165Winkler, Michael 33 2018 Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Zbl 1404.35464Winkler, Michael 32 2018 Stabilization in the logarithmic Keller-Segel system. Zbl 1391.35066Winkler, Michael; Yokota, Tomomi 24 2018 Singular structure formation in a degenerate haptotaxis model involving myopic diffusion. Zbl 1391.35065Winkler, Michael 23 2018 Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains. Zbl 1403.35128Cao, Xinru; Winkler, Michael 7 2018 Global solvability and explicit bounds for non-local adhesion models. Zbl 1406.35430Hillen, T.; Painter, K. J.; Winkler, M. 7 2018 FiberSCIP – a shared memory parallelization of SCIP. Zbl 07271621Shinano, Yuji; Heinz, Stefan; Vigerske, Stefan; Winkler, Michael 2 2018 Cross-diffusion models: analytic and multiscale problems. Zbl 1408.35078Bellomo, N.; Tao, Y.; Winkler, M. 2 2018 One-dimensional super-fast diffusion: persistence versus extinction revisited – extinction at spatial infinity. Zbl 1388.35116Winkler, Michael 1 2018 How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Zbl 1356.35071Winkler, Michael 135 2017 Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068Tao, Youshan; Winkler, Michael 72 2017 A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data. Zbl 1373.35166Lankeit, Johannes; Winkler, Michael 68 2017 Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 06761738Tao, Youshan; Winkler, Michael 63 2017 Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems. Zbl 1377.35158Winkler, Michael 51 2017 A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166Bellomo, Nicola; Winkler, Michael 49 2017 Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044Bellomo, Nicola; Winkler, Michael 48 2017 Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation. Zbl 1370.35059Winkler, Michael 41 2017 Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity. Zbl 1382.35048Winkler, Michael 26 2017 Global bounded solutions in a two-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1364.35124Cieślak, Tomasz; Winkler, Michael 24 2017 Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1367.35033Cieślak, Tomasz; Winkler, Michael 22 2017 Global weak solutions to a strongly degenerate haptotaxis model. Zbl 1390.35164Winkler, Michael; Surulescu, Christina 14 2017 Nonexistence of nonconstant steady-state solutions in a triangular cross-diffusion model. Zbl 1372.35038Lou, Yuan; Tao, Youshan; Winkler, Michael 9 2017 Slow growth of solutions of superfast diffusion equations with unbounded initial data. Zbl 1386.35178Fila, Marek; Winkler, Michael 6 2017 On a degenerate nonlocal parabolic problem describing infinite dimensional replicator dynamics. Zbl 1365.35195Kavallaris, Nikos I.; Lankeit, Johannes; Winkler, Michael 4 2017 Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Zbl 1351.35239Winkler, Michael 183 2016 Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Zbl 1345.35117Bai, Xueli; Winkler, Michael 169 2016 ...and 106 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,478 Authors 158 Winkler, Michael 74 Mu, Chunlai 52 Tao, Youshan 43 Zheng, Pan 41 Zheng, Jiashan 39 Wang, Liangchen 35 Yokota, Tomomi 34 Liu, Bin 33 Zheng, Sining 31 Lankeit, Johannes 30 Wang, Zhian 29 Wang, Yifu 26 Ren, Guoqiang 25 Xiang, Zhaoyin 24 Jin, Haiyang 22 Lin, Ke 22 Shen, Wenxian 21 Wang, Qi 21 Xiang, Tian 20 Fila, Marek 20 Fujie, Kentaro 20 Kang, Kyungkeun 19 Mizukami, Masaaki 19 Viglialoro, Giuseppe 18 Wang, Wei 17 Hu, Xuegang 17 Liu, Ji 17 Stinner, Christian 16 Elaiw, Ahmed M. 16 Wang, Yulan 15 Black, Tobias 15 Negreanu, Mihaela 15 Surulescu, Christina 14 Bellomo, Nicola 14 Cao, Xinru 14 Jin, Chunhua 14 Liu, Chein-Shan 14 Yanagida, Eiji 13 Jiang, Jie 13 Liu, Zuhan 13 Qiu, Shuyan 13 Tello, José Ignacio 13 Wang, Yilong 13 Yin, Jingxue 13 Zhang, Qian 12 Li, Xie 12 Painter, Kevin J. 12 Zhang, Qingshan 12 Zhao, Jie 11 Guo, Shangjiang 11 Li, Dan 11 Li, Yuxiang 11 Salako, Rachidi Bolaji 10 Cieślak, Tomasz 10 Dai, Feng 10 Fuest, Mario 10 Guillén González, Francisco M. 10 Hillen, Thomas 10 Ishida, Sachiko 10 Ke, Yuanyuan 10 Lee, Jihoon 10 Li, Yan 10 Li, Zhongping 10 Morales-Rodrigo, Cristian 10 Rueda-Gómez, Diego Armando 10 Souplet, Philippe 10 Tu, Xinyu 10 Zhou, Ling 9 Fu, Shengmao 9 Laurençot, Philippe 9 Li, Jing 9 Liu, Zhengrong 9 Pan, Xu 9 Shangerganesh, Lingeshwaran 9 Shi, Junping 9 Villamizar-Roa, Elder Jesús 8 Alshamrani, Noura H. 8 Ding, Mengyao 8 Rodríguez-Bellido, Maria Angeles 8 Suárez, Antonio 8 Wu, Sainan 8 Xing, Jie 8 Zhigun, Anna 7 Ahn, Jaewook 7 Carrillo de la Plata, José Antonio 7 Chiyo, Yutaro 7 Hui, Kin Ming 7 Ma, Manjun 7 Tao, Xueyan 7 Wang, Liangwei 7 Wrzosek, Dariusz M. 7 Yoon, Changwook 7 Yu, Hao 7 Zhang, Zhengce 7 Zhao, Kun 7 Zhao, Xiangdong 7 Zhou, Shuangshuang 6 Baghaei, Khadijeh 6 Chae, Myeongju 6 Chaplain, Mark A. 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