## Winkler, Michael

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 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: 213 Publications since 2001 2 Contributions as Editor Co-Authors: 65 Co-Authors with 131 Joint Publications 2,033 Co-Co-Authors
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### Co-Authors

 84 single-authored 36 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 Vazquez, Juan Luis 4 Wrzosek, Dariusz M. 4 Yokota, Tomomi 3 Cieślak, Tomasz 3 Fujie, Kentaro 3 Lou, Yuan 3 Surulescu, Christina 2 Brunovský, Pavol 2 Černý, Aleš 2 Heinz, Stefan 2 Jüngel, Ansgar 2 Li, Genglin 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 I. 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 Rodriguez, Nancy Y. 1 Shinano, Yuji 1 Soler, Juan S. 1 Suen, Anthony 1 Taskinen, Jari 1 Trescases, Ariane 1 Velázquez, Juan J. L. 1 Vigerske, Stefan 1 Xue, Chuan
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### Serials

 20 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 7 Mathematical Methods in the Applied Sciences 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Communications in Partial Differential Equations 7 Discrete and Continuous Dynamical Systems 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. Series B 4 Communications on Pure and Applied Analysis 3 Archive for Rational Mechanics and Analysis 3 Journal of Mathematical Biology 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 European Journal of Applied Mathematics 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Calculus of Variations and Partial Differential Equations 2 Communications in Mathematical Physics 2 Israel Journal of Mathematics 2 Applied Mathematics and Optimization 2 Journal of Functional Analysis 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Nachrichten 2 Transactions of the American Mathematical Society 2 Acta Applicandae Mathematicae 2 Applied Mathematics Letters 2 Journal of Nonlinear Science 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Mathematical Sciences 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Advances in Nonlinear Analysis 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal d’Analyse Mathématique 1 Mathematical Biosciences 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Mathematische Zeitschrift 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Zeitschrift für Analysis und ihre Anwendungen 1 Asymptotic Analysis 1 IMRN. International Mathematics Research Notices 1 Acta Mathematica Universitatis Comenianae. New Series 1 SIAM Journal on Applied Mathematics 1 INFORMS Journal on Computing 1 Journal of Mathematical Fluid Mechanics 1 Acta Mathematica Sinica. English Series 1 Advanced Nonlinear Studies 1 Analysis and Applications (Singapore) 1 Oberwolfach Reports 1 Discrete and Continuous Dynamical Systems. Series S 1 International Journal of Dynamical Systems and Differential Equations 1 Mathematical Programming Computation 1 Science China. Mathematics 1 Transactions of the American Mathematical Society. Series B 1 SN Partial Differential Equations and Applications
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### Fields

 209 Partial differential equations (35-XX) 143 Biology and other natural sciences (92-XX) 12 Fluid mechanics (76-XX) 7 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)

### Citations contained in zbMATH Open

198 Publications have been cited 9,962 times in 1,719 Documents Cited by Year
Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model. Zbl 1190.92004
Winkler, Michael
2010
Boundedness vs. blow-up in a chemotaxis system. Zbl 1085.35065
Horstmann, Dirk; Winkler, Michael
2005
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.
2015
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. Zbl 1326.35053
Winkler, Michael
2013
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity. Zbl 1382.35127
Tao, Youshan; Winkler, Michael
2012
Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source. Zbl 1290.35139
Winkler, Michael
2010
A chemotaxis system with logistic source. Zbl 1121.37068
Tello, J. Ignacio; Winkler, Michael
2007
Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Zbl 1236.35192
Winkler, Michael
2012
Stabilization in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1293.35220
Winkler, Michael
2014
Does a volume-filling effect always prevent chemotactic collapse? Zbl 1182.35220
Winkler, Michael
2010
Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction. Zbl 1241.35028
Winkler, Michael
2011
Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening. Zbl 1293.35048
Winkler, Michael
2014
Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Zbl 1351.35239
Winkler, Michael
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
2012
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Zbl 1345.35117
Bai, Xueli; Winkler, Michael
2016
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity. Zbl 1333.35104
Winkler, Michael
2015
Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect. Zbl 1183.92012
Winkler, Michael; Djie, Kianhwa C.
2010
Finite-time blow-up in a quasilinear system of chemotaxis. Zbl 1136.92006
Cieślak, Tomasz; Winkler, Michael
2008
Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Zbl 1283.35154
Tao, Youshan; Winkler, Michael
2013
Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion. Zbl 1301.35189
Stinner, Christian; Surulescu, Christina; Winkler, Michael
2014
Chemotaxis with logistic source: very weak global solutions and their boundedness properties. Zbl 1147.92005
Winkler, Michael
2008
How far can chemotactic cross-diffusion enforce exceeding carrying capacities? Zbl 1311.35040
Winkler, Michael
2014
A chemotaxis-haptotaxis model: the roles of nonlinear diffusion and logistic source. Zbl 1259.35210
Tao, Youshan; Winkler, Michael
2011
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Zbl 1356.35071
Winkler, Michael
2017
Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Zbl 1276.35105
Tao, Youshan; Winkler, Michael
2012
Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Zbl 1328.35084
Tao, Youshan; Winkler, Michael
2015
Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity. Zbl 1205.35037
Winkler, Michael
2010
Global solutions in a fully parabolic chemotaxis system with singular sensitivity. Zbl 1291.92018
Winkler, Michael
2011
Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion. Zbl 1328.35103
Tao, Youshan; Winkler, Michael
2015
Stabilization in a two-species chemotaxis system with a logistic source. Zbl 1260.92014
Tello, J. I.; Winkler, M.
2012
Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048
Winkler, Michael
2018
Competitive exclusion in a two-species chemotaxis model. Zbl 1319.92050
Stinner, C.; Tello, J. I.; Winkler, M.
2014
Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities. Zbl 1330.35202
Winkler, Michael
2015
Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Zbl 1356.35054
Tao, Youshan; Winkler, Michael
2016
A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. Zbl 1408.35132
Winkler, Michael
2019
Stabilization in a chemotaxis model for tumor invasion. Zbl 1322.35059
Yokota, Tomomi; Winkler, Michael; Ito, Akio; Fujie, Kentarou
2016
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
2014
Convergence of a cancer invasion model to a logistic chemotaxis model. Zbl 1263.35204
Hillen, Thomas; Painter, Kevin J.; Winkler, Michael
2013
Global weak solutions in a chemotaxis system with large singular sensitivity. Zbl 1268.35072
Stinner, Christian; Winkler, Michael
2011
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068
Tao, Youshan; Winkler, Michael
2017
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2018
Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals. Zbl 1329.35075
Winkler, Michael; Tao, Youshan
2015
A fourth-order parabolic equation modeling epitaxial thin film growth. Zbl 1029.35110
King, Belinda B.; Stein, Oliver; Winkler, Michael
2003
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
2017
A critical exponent in a degenerate parabolic equation. Zbl 1007.35043
Winkler, Michael
2002
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
2015
A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240
Winkler, Michael
2018
Dominance of chemotaxis in a chemotaxis-haptotaxis model. Zbl 1293.35047
Tao, Youshan; Winkler, Michael
2014
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
2016
Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 06761738
Tao, Youshan; Winkler, Michael
2017
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Zbl 1395.35038
Winkler, Michael
2018
Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems. Zbl 1377.35158
Winkler, Michael
2017
A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166
Bellomo, Nicola; Winkler, Michael
2017
Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model. Zbl 1312.35171
Tao, Youshan; Winkler, Michael
2014
Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity. Zbl 1329.35011
Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi
2015
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
2014
Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044
Bellomo, Nicola; Winkler, Michael
2017
Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity? Zbl 1409.35047
Winkler, Michael
2018
Persistence of mass in a chemotaxis system with logistic source. Zbl 1321.35084
Tao, Youshan; Winkler, Michael
2015
Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation. Zbl 1370.35059
Winkler, Michael
2017
Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization. Zbl 1392.35042
Espejo, Elio; Winkler, Michael
2018
The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1397.35322
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2018
Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption. Zbl 1378.35165
Winkler, Michael
2018
Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052
Winkler, Michael
2019
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
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
2019
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Zbl 1404.35464
Winkler, Michael
2018
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
2012
Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations. Zbl 1441.35079
Winkler, Michael
2020
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
2019
Global existence and uniform boundedness of smooth solutions to a cross-diffusion system with equal diffusion rates. Zbl 1332.35172
Lou, Yuan; Winkler, Michael
2015
Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity. Zbl 1382.35048
Winkler, Michael
2017
Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612
Winkler, Michael
2019
Facing low regularity in chemotaxis systems. Zbl 1436.92004
Lankeit, Johannes; Winkler, Michael
2020
Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065
Winkler, Michael
2020
Stabilization in the logarithmic Keller-Segel system. Zbl 1391.35066
Winkler, Michael; Yokota, Tomomi
2018
Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132
Tao, Youshan; Winkler, Michael
2020
Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1367.35033
Cieślak, Tomasz; Winkler, Michael
2017
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
2017
Global solutions in higher dimensions to a fourth-order parabolic equation modeling epitaxial thin-film growth. Zbl 1258.35192
Winkler, Michael
2011
Singular structure formation in a degenerate haptotaxis model involving myopic diffusion. Zbl 1391.35065
Winkler, Michael
2018
Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. Zbl 1295.35098
Lou, Yuan; Tao, Youshan; Winkler, Michael
2014
Convergence rate for a parabolic equation with supercritical nonlinearity. Zbl 1087.35049
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2005
A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480
Tao, Youshan; Winkler, Michael
2020
Grow up rate of solutions for a supercritical semilinear diffusion equation. Zbl 1072.35042
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2004
A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181
Tao, Youshan; Winkler, Michael
2019
Singularity formation in chemotaxis systems with volume-filling effect. Zbl 1255.35213
Wang, Zhi-An; Winkler, Michael; Wrzosek, Dariusz
2011
Optimal lower bound of the grow-up rate for a supercritical parabolic equation. Zbl 1102.35017
Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji
2006
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $${n\geq 3}$$. Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
2019
Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027
Quittner, Pavol; Souplet, Philippe; Winkler, Michael
2004
Rate of convergence to Barenblatt profiles for the fast diffusion equation. Zbl 1315.76032
Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji
2012
Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems? Zbl 1483.35294
Winkler, Michael
2021
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
2019
Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Zbl 1428.35611
Winkler, Michael
2019
Global solvability in a three-dimensional Keller-Segel-Stokes system involving arbitrary superlinear logistic degradation. Zbl 1466.92020
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2021
The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2019
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
2021
Amorphous molecular beam epitaxy: global solutions and absorbing sets. Zbl 1120.35045
Stein, O.; Winkler, M.
2005
Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension. Zbl 1411.35146
Tao, Youshan; Winkler, Michael
2019
Large time behavior of solutions to degenerate parabolic equations with absorption. Zbl 0980.35077
Winkler, Michael
2001
Reaction-driven relaxation in three-dimensional Keller-Segel-Navier-Stokes interaction. Zbl 1486.35102
Winkler, Michael
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
2022
Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system. Zbl 1496.35228
Tao, Youshan; Winkler, Michael
2022
Small-signal solutions of a two-dimensional doubly degenerate taxis system modeling bacterial motion in nutrient-poor environments. Zbl 1479.35224
Winkler, Michael
2022
Unlimited growth in logarithmic Keller-Segel systems. Zbl 1480.35383
Winkler, Michael
2022
Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary. Zbl 1481.35023
Lankeit, Johannes; Winkler, Michael
2022
Nonnegative solutions to a doubly degenerate nutrient taxis system. Zbl 1483.35127
Li, Genglin; Winkler, Michael
2022
Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy. Zbl 1484.35363
Tao, Youshan; Winkler, Michael
2022
Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. Zbl 07544554
Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M.
2022
Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems? Zbl 1483.35294
Winkler, Michael
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
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
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
2021
Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. Zbl 1466.35060
Winkler, Michael
2021
Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity. Zbl 1453.35115
Winkler, Michael
2021
Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Zbl 1458.35076
Tao, Youshan; Winkler, Michael
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
2021
Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation. Zbl 1468.35220
Winkler, Michael
2021
Small-density solutions in Keller-Segel systems involving rapidly decaying diffusivities. Zbl 1471.35064
Ding, Mengyao; Winkler, Michael
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
2021
Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. Zbl 1479.35120
Tao, Youshan; Winkler, Michael
2021
Taxis-driven formation of singular hotspots in a May-Nowak-type model for virus infection. Zbl 1461.35201
Tao, Youshan; Winkler, Michael
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
2021
The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. Zbl 1465.35378
Tao, Youshan; Winkler, Michael
2021
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
2020
Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations. Zbl 1441.35079
Winkler, Michael
2020
Facing low regularity in chemotaxis systems. Zbl 1436.92004
Lankeit, Johannes; Winkler, Michael
2020
Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065
Winkler, Michael
2020
Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132
Tao, Youshan; Winkler, Michael
2020
A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480
Tao, Youshan; Winkler, Michael
2020
Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250
Li, Genglin; Tao, Youshan; Winkler, Michael
2020
Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system. Zbl 1459.92019
Winkler, Michael
2020
Mathematical analysis of two competing cancer cell migration mechanisms driven by interstitial fluid flow. Zbl 1442.35469
Evje, Steinar; Winkler, Michael
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
2020
Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation. Zbl 1451.35226
Rodríguez, Nancy; Winkler, Michael
2020
Boundedness in a two-dimensional Keller-Segel-Navier-Stokes system involving a rapidly diffusing repulsive signal. Zbl 1432.92021
Winkler, Michael
2020
Chemotaxis systems in complex frameworks: pattern formation, qualitative analysis and blowup prevention. Zbl 1451.92062
Bellomo, N.; Tao, Y.; Winkler, M.
2020
Single-point blow-up in the Cauchy problem for the higher-dimensional Keller-Segel system. Zbl 1452.35227
Winkler, Michael
2020
Refined regularity and stabilization properties in a degenerate haptotaxis system. Zbl 1437.35434
Winkler, Michael; Stinner, Christian
2020
A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. Zbl 1408.35132
Winkler, Michael
2019
Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052
Winkler, Michael
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
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
2019
Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612
Winkler, Michael
2019
A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181
Tao, Youshan; Winkler, Michael
2019
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $${n\geq 3}$$. Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
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
2019
Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Zbl 1428.35611
Winkler, Michael
2019
The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2019
Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension. Zbl 1411.35146
Tao, Youshan; Winkler, Michael
2019
How strong singularities can be regularized by logistic degradation in the Keller-Segel system? Zbl 1437.35004
Winkler, Michael
2019
Boundedness and stabilization in a population model with cross-diffusion for one species. Zbl 1439.35275
Tao, Youshan; Winkler, Michael
2019
Boundedness in a chemotaxis-May-Nowak model for virus dynamics with mildly saturated chemotactic sensitivity. Zbl 1423.35172
Winkler, Michael
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
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
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
2019
Migration-driven benefit in a two-species nutrient taxis system. Zbl 1425.92033
Krzyżanowski, Piotr; Winkler, Michael; Wrzosek, Dariusz
2019
Structure-driven fix-and-propagate heuristics for mixed integer programming. Zbl 1432.90091
Gamrath, Gerald; Berthold, Timo; Heinz, Stefan; Winkler, Michael
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
2019
Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048
Winkler, Michael
2018
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2018
A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240
Winkler, Michael
2018
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Zbl 1395.35038
Winkler, Michael
2018
Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity? Zbl 1409.35047
Winkler, Michael
2018
Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization. Zbl 1392.35042
Espejo, Elio; Winkler, Michael
2018
The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1397.35322
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2018
Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption. Zbl 1378.35165
Winkler, Michael
2018
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Zbl 1404.35464
Winkler, Michael
2018
Stabilization in the logarithmic Keller-Segel system. Zbl 1391.35066
Winkler, Michael; Yokota, Tomomi
2018
Singular structure formation in a degenerate haptotaxis model involving myopic diffusion. Zbl 1391.35065
Winkler, Michael
2018
Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains. Zbl 1403.35128
Cao, Xinru; Winkler, Michael
2018
Global solvability and explicit bounds for non-local adhesion models. Zbl 1406.35430
Hillen, T.; Painter, K. J.; Winkler, M.
2018
FiberSCIP – a shared memory parallelization of SCIP. Zbl 07271621
Shinano, Yuji; Heinz, Stefan; Vigerske, Stefan; Winkler, Michael
2018
Cross-diffusion models: analytic and multiscale problems. Zbl 1408.35078
Bellomo, N.; Tao, Y.; Winkler, M.
2018
One-dimensional super-fast diffusion: persistence versus extinction revisited – extinction at spatial infinity. Zbl 1388.35116
Winkler, Michael
2018
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Zbl 1356.35071
Winkler, Michael
2017
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068
Tao, Youshan; Winkler, Michael
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
2017
Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 06761738
Tao, Youshan; Winkler, Michael
2017
Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems. Zbl 1377.35158
Winkler, Michael
2017
A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166
Bellomo, Nicola; Winkler, Michael
2017
Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044
Bellomo, Nicola; Winkler, Michael
2017
Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation. Zbl 1370.35059
Winkler, Michael
2017
Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity. Zbl 1382.35048
Winkler, Michael
2017
Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1367.35033
Cieślak, Tomasz; Winkler, Michael
2017
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
2017
Global weak solutions to a strongly degenerate haptotaxis model. Zbl 1390.35164
Winkler, Michael; Surulescu, Christina
2017
Nonexistence of nonconstant steady-state solutions in a triangular cross-diffusion model. Zbl 1372.35038
Lou, Yuan; Tao, Youshan; Winkler, Michael
2017
Slow growth of solutions of superfast diffusion equations with unbounded initial data. Zbl 1386.35178
Fila, Marek; Winkler, Michael
2017
On a degenerate nonlocal parabolic problem describing infinite dimensional replicator dynamics. Zbl 1365.35195
Kavallaris, Nikos I.; Lankeit, Johannes; Winkler, Michael
2017
Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Zbl 1351.35239
Winkler, Michael
2016
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Zbl 1345.35117
Bai, Xueli; Winkler, Michael
2016
Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Zbl 1356.35054
Tao, Youshan; Winkler, Michael
2016
Stabilization in a chemotaxis model for tumor invasion. Zbl 1322.35059
Yokota, Tomomi; Winkler, Michael; Ito, Akio; Fujie, Kentarou
2016
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
2016
Chemotactic cross-diffusion in complex frameworks. Zbl 06646361
Winkler, M.
2016
Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation. Zbl 1349.35168
Fila, Marek; Winkler, Michael
2016
Rate of convergence to separable solutions of the fast diffusion equation. Zbl 1348.35120
Fila, Marek; Winkler, Michael
2016
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.
2015
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity. Zbl 1333.35104
Winkler, Michael
2015
...and 98 more Documents
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### Cited by 1,387 Authors

 152 Winkler, Michael 73 Mu, Chunlai 51 Tao, Youshan 41 Zheng, Pan 40 Zheng, Jiashan 35 Yokota, Tomomi 34 Wang, Liangchen 33 Zheng, Sining 31 Lankeit, Johannes 29 Wang, Yifu 29 Wang, Zhian 25 Xiang, Zhaoyin 24 Ren, Guoqiang 23 Jin, Haiyang 22 Lin, Ke 21 Shen, Wenxian 20 Fila, Marek 20 Fujie, Kentaro 20 Kang, Kyungkeun 20 Xiang, Tian 19 Mizukami, Masaaki 19 Viglialoro, Giuseppe 18 Wang, Wei 17 Liu, Ji 17 Stinner, Christian 16 Hu, Xuegang 16 Wang, Yulan 15 Black, Tobias 15 Negreanu, Mihaela 14 Bellomo, Nicola 14 Cao, Xinru 14 Elaiw, Ahmed M. 14 Surulescu, Christina 14 Yanagida, Eiji 13 Jiang, Jie 13 Liu, Chein-Shan 13 Tello, José Ignacio 13 Wang, Yilong 13 Yin, Jingxue 13 Zhang, Qian 12 Jin, Chunhua 12 Li, Xie 12 Liu, Zuhan 12 Painter, Kevin J. 12 Qiu, Shuyan 12 Zhang, Qingshan 12 Zhao, Jie 11 Guo, Shangjiang 11 Li, Dan 11 Li, Yuxiang 11 Salako, Rachidi Bolaji 10 Cieślak, Tomasz 10 Fuest, Mario 10 Hillen, Thomas 10 Ishida, Sachiko 10 Ke, Yuanyuan 10 Lee, Jihoon 10 Li, Yan 10 Morales-Rodrigo, Cristian 10 Souplet, Philippe 10 Tu, Xinyu 10 Zhou, Ling 9 Dai, Feng 9 Fu, Shengmao 9 Laurençot, Philippe 9 Li, Jing 9 Liu, Zhengrong 9 Rueda-Gómez, Diego Armando 9 Shangerganesh, Lingeshwaran 9 Shi, Junping 8 Alshamrani, Noura H. 8 Ding, Mengyao 8 Guillén González, Francisco M. 8 Li, Zhongping 8 Pan, Xu 8 Suárez, Antonio 8 Villamizar-Roa, Elder Jesús 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 Rodríguez-Bellido, Maria Angeles 7 Wang, Liangwei 7 Yoon, Changwook 7 Yu, Hao 7 Zhao, Xiangdong 7 Zhou, Shuangshuang 6 Baghaei, Khadijeh 6 Chae, Myeongju 6 Chaplain, Mark A. J. 6 Issa, Tahir Bachar 6 Jüngel, Ansgar 6 Liu, Suying 6 Lv, Wenbin 6 Lyu, Wenbin 6 Marras, Monica ...and 1,287 more Authors
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### Cited in 204 Serials

 185 Journal of Differential Equations 159 Journal of Mathematical Analysis and Applications 94 Nonlinear Analysis. Real World Applications 92 Discrete and Continuous Dynamical Systems. Series B 82 ZAMP. Zeitschrift für angewandte Mathematik und Physik 78 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 62 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 61 Discrete and Continuous Dynamical Systems 46 Applied Mathematics Letters 33 Computers & Mathematics with Applications 32 Acta Applicandae Mathematicae 30 Mathematical Methods in the Applied Sciences 29 SIAM Journal on Mathematical Analysis 27 Applicable Analysis 26 Boundary Value Problems 25 Communications on Pure and Applied Analysis 24 Nonlinearity 23 Calculus of Variations and Partial Differential Equations 23 Discrete and Continuous Dynamical Systems. Series S 20 Journal of Mathematical Physics 16 Journal of Evolution Equations 15 Journal of Mathematical Biology 15 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 14 Journal of Dynamics and Differential Equations 13 Communications in Partial Differential Equations 12 NoDEA. Nonlinear Differential Equations and Applications 11 Journal of Functional Analysis 11 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 SIAM Journal on Applied Mathematics 10 Journal of Theoretical Biology 9 Applied Mathematics and Computation 9 Mathematische Annalen 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Mathematical Biosciences and Engineering 9 Advances in Nonlinear Analysis 8 Electronic Journal of Differential Equations (EJDE) 8 Advances in Difference Equations 7 Journal of Mathematical Fluid Mechanics 7 International Journal of Biomathematics 6 Bulletin of Mathematical Biology 6 Annali di Matematica Pura ed Applicata. Serie Quarta 6 Proceedings of the American Mathematical Society 6 Physica D 6 Discrete Dynamics in Nature and Society 6 Communications in Nonlinear Science and Numerical Simulation 6 Kinetic and Related Models 6 AIMS Mathematics 6 Electronic Research Archive 5 Applied Mathematics and Optimization 5 Results in Mathematics 5 Transactions of the American Mathematical Society 5 European Journal of Applied Mathematics 5 Journal of Nonlinear Science 5 Acta Mathematica Scientia. Series B. (English Edition) 5 Science China. Mathematics 5 SN Partial Differential Equations and Applications 4 Archive for Rational Mechanics and Analysis 4 Communications in Mathematical Physics 4 Journal of Computational Physics 4 Applied Numerical Mathematics 4 Journal of Scientific Computing 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Journal of Inequalities and Applications 4 Advanced Nonlinear Studies 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Journal of Applied Mathematics and Computing 4 Analysis and Applications (Singapore) 4 Mathematics in Engineering 3 Computer Methods in Applied Mechanics and Engineering 3 Journal d’Analyse Mathématique 3 Indiana University Mathematics Journal 3 Journal of Computational and Applied Mathematics 3 Mathematische Nachrichten 3 Monatshefte für Mathematik 3 Applied Mathematics. Series B (English Edition) 3 Abstract and Applied Analysis 3 Acta Mathematica Sinica. English Series 3 Journal of Dynamical and Control Systems 3 Acta Mathematica Scientia. Series A. (Chinese Edition) 3 SIAM Journal on Applied Dynamical Systems 3 Mathematics in Applied Sciences and Engineering 2 Israel Journal of Mathematics 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Physica A 2 Rocky Mountain Journal of Mathematics 2 Chaos, Solitons and Fractals 2 Archiv der Mathematik 2 Czechoslovak Mathematical Journal 2 Duke Mathematical Journal 2 Funkcialaj Ekvacioj. Serio Internacia 2 Numerische Mathematik 2 Osaka Journal of Mathematics 2 Quarterly of Applied Mathematics 2 SIAM Journal on Numerical Analysis 2 Acta Mathematicae Applicatae Sinica. English Series 2 Japan Journal of Industrial and Applied Mathematics 2 Applications of Mathematics 2 Applied Mathematical Modelling 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences ...and 104 more Serials
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### Cited in 32 Fields

 1,629 Partial differential equations (35-XX) 1,255 Biology and other natural sciences (92-XX) 119 Fluid mechanics (76-XX) 88 Numerical analysis (65-XX) 48 Ordinary differential equations (34-XX) 28 Dynamical systems and ergodic theory (37-XX) 25 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Calculus of variations and optimal control; optimization (49-XX) 23 Statistical mechanics, structure of matter (82-XX) 22 Probability theory and stochastic processes (60-XX) 17 Operator theory (47-XX) 14 Mechanics of deformable solids (74-XX) 12 Integral equations (45-XX) 10 Systems theory; control (93-XX) 9 Real functions (26-XX) 8 Differential geometry (53-XX) 7 Functional analysis (46-XX) 6 Global analysis, analysis on manifolds (58-XX) 4 Potential theory (31-XX) 4 Operations research, mathematical programming (90-XX) 3 General and overarching topics; collections (00-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Difference and functional equations (39-XX) 2 Mechanics of particles and systems (70-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)