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## Winkler, Michael

Compute Distance To:
 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: 195 Publications since 2001
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#### Co-Authors

 77 single-authored 32 Tao, Youshan 22 Fila, Marek 10 Yanagida, Eiji 7 Stinner, Christian 6 Bellomo, Nicola 6 Wang, Yulan 6 Xiang, Zhaoyin 5 King, John Robert 5 Tello, José Ignacio 4 Hillen, Thomas 4 Lankeit, Johannes 4 Painter, Kevin J. 4 Souplet, Philippe 4 Vazquez, Juan Luis 4 Wrzosek, Dariusz M. 4 Yokota, Tomomi 3 Cieślak, Tomasz 3 Fujie, Kentarou 3 Lou, Yuan 3 Surulescu, Christina 2 Brunovský, Pavol 2 Černý, Aleš 2 Heinz, Stefan 2 Jüngel, Ansgar 2 Stein, Oliver T. 2 Wang, Zhian 1 Bai, Xueli 1 Bellouquid, Abdelghani 1 Berthold, Timo 1 Cao, Xinru 1 Cosner, Chris 1 Deutsch, Andreas 1 Ding, Mengyao 1 Djie, Kianhwa C. 1 Dreyer, Wolfgang 1 Espejo, Elio E. 1 Evje, Steinar 1 Gamrath, Gerald 1 Horstmann, Dirk 1 Huth, Robert 1 Ito, Akio 1 Kavallaris, Nikos I. 1 King, Belinda Batten 1 Krzyżanowski, Piotr 1 Li, Genglin 1 Li, Tong 1 Mielke, Alexander 1 Quittner, Pavol 1 Rehberg, Joachim 1 Rodriguez, Nancy Y. 1 Shinano, Yuji 1 Suen, Anthony 1 Taskinen, Jari 1 Velázquez, Juan J. L. 1 Vigerske, Stefan 1 Xue, Chuan
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#### Serials

 19 Journal of Differential Equations 11 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 10 SIAM Journal on Mathematical Analysis 9 Nonlinearity 8 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 6 Discrete and Continuous Dynamical Systems 5 Journal of Mathematical Analysis and Applications 5 Mathematische Annalen 5 NoDEA. Nonlinear Differential Equations and Applications 5 Advances in Differential Equations 4 Indiana University Mathematics Journal 4 Journal of Dynamics and Differential Equations 4 Nonlinear Analysis. Real World Applications 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 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Journal of Evolution Equations 3 Discrete and Continuous Dynamical Systems. Series B 3 Communications on Pure and Applied Analysis 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 de Mathématiques Pures et Appliquées. Neuvième Série 2 Journal of Nonlinear Science 2 Calculus of Variations and Partial Differential Equations 2 Journal of the European Mathematical Society (JEMS) 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Advances in Nonlinear Analysis 1 Communications in Mathematical Physics 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 Advanced Nonlinear Studies 1 Communications in Mathematical Sciences 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
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#### Fields

 188 Partial differential equations (35-XX) 125 Biology and other natural sciences (92-XX) 11 Fluid mechanics (76-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Dynamical systems and ergodic theory (37-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 Mechanics of deformable solids (74-XX) 2 Operations research, mathematical programming (90-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH Open

173 Publications have been cited 7,450 times in 1,329 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
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. Zbl 1326.35053
Winkler, Michael
2013
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 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
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
Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Zbl 1351.35239
Winkler, Michael
2016
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
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity. Zbl 1333.35104
Winkler, Michael
2015
Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Zbl 1283.35154
Tao, Youshan; Winkler, Michael
2013
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
Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion. Zbl 1301.35189
Stinner, Christian; Surulescu, Christina; Winkler, Michael
2014
A chemotaxis-haptotaxis model: the roles of nonlinear diffusion and logistic source. Zbl 1259.35210
Tao, Youshan; Winkler, Michael
2011
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Zbl 1345.35117
Bai, Xueli; Winkler, Michael
2016
Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Zbl 1276.35105
Tao, Youshan; Winkler, Michael
2012
Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity. Zbl 1205.35037
Winkler, Michael
2010
Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Zbl 1328.35084
Tao, Youshan; Winkler, Michael
2015
Global solutions in a fully parabolic chemotaxis system with singular sensitivity. Zbl 1291.92018
Winkler, Michael
2011
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Zbl 1356.35071
Winkler, Michael
2017
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
Competitive exclusion in a two-species chemotaxis model. Zbl 1319.92050
Stinner, C.; Tello, J. I.; Winkler, M.
2014
Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Zbl 1356.35054
Tao, Youshan; Winkler, Michael
2016
Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities. Zbl 1330.35202
Winkler, Michael
2015
Stabilization in a chemotaxis model for tumor invasion. Zbl 1322.35059
Yokota, Tomomi; Winkler, Michael; Ito, Akio; Fujie, Kentarou
2016
Global weak solutions in a chemotaxis system with large singular sensitivity. Zbl 1268.35072
Stinner, Christian; Winkler, Michael
2011
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
Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048
Winkler, Michael
2018
Convergence of a cancer invasion model to a logistic chemotaxis model. Zbl 1263.35204
Hillen, Thomas; Painter, Kevin J.; Winkler, Michael
2013
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
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068
Tao, Youshan; Winkler, Michael
2017
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 solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2018
A fourth-order parabolic equation modeling epitaxial thin film growth. Zbl 1029.35110
King, Belinda B.; Stein, Oliver; Winkler, Michael
2003
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
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
Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model. Zbl 1312.35171
Tao, Youshan; Winkler, Michael
2014
Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems. Zbl 1377.35158
Winkler, Michael
2017
Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals. Zbl 1329.35075
Winkler, Michael; Tao, Youshan
2015
A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166
Bellomo, Nicola; Winkler, Michael
2017
A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240
Winkler, Michael
2018
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
Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity. Zbl 1329.35011
Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi
2015
Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 06761738
Tao, Youshan; Winkler, Michael
2017
Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044
Bellomo, Nicola; Winkler, Michael
2017
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Zbl 1395.35038
Winkler, Michael
2018
Persistence of mass in a chemotaxis system with logistic source. Zbl 1321.35084
Tao, Youshan; Winkler, Michael
2015
Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity? Zbl 1409.35047
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
Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization. Zbl 1392.35042
Espejo, Elio; Winkler, Michael
2018
Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation. Zbl 1370.35059
Winkler, Michael
2017
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
Convergence rate for a parabolic equation with supercritical nonlinearity. Zbl 1087.35049
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2005
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Zbl 1404.35464
Winkler, Michael
2018
Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity. Zbl 1382.35048
Winkler, Michael
2017
Grow up rate of solutions for a supercritical semilinear diffusion equation. Zbl 1072.35042
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2004
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
Singularity formation in chemotaxis systems with volume-filling effect. Zbl 1255.35213
Wang, Zhi-An; Winkler, Michael; Wrzosek, Dariusz
2011
Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052
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
Initial blow-up rates and universal bounds for nonlinear heat equations. Zbl 1044.35027
Quittner, Pavol; Souplet, Philippe; Winkler, Michael
2004
Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. Zbl 1295.35098
Lou, Yuan; Tao, Youshan; Winkler, Michael
2014
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 solutions in higher dimensions to a fourth-order parabolic equation modeling epitaxial thin-film growth. Zbl 1258.35192
Winkler, Michael
2011
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 generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612
Winkler, Michael
2019
Singular structure formation in a degenerate haptotaxis model involving myopic diffusion. Zbl 1391.35065
Winkler, Michael
2018
Rate of convergence to Barenblatt profiles for the fast diffusion equation. Zbl 1315.76032
Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji
2012
Stabilization in the logarithmic Keller-Segel system. Zbl 1391.35066
Winkler, Michael; Yokota, Tomomi
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
2020
A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181
Tao, Youshan; 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 of solutions to degenerate parabolic equations with absorption. Zbl 0980.35077
Winkler, Michael
2001
Nonuniqueness in the quenching problem. Zbl 1132.35049
Winkler, Michael
2007
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $${n\geq 3}$$. Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
2019
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
Amorphous molecular beam epitaxy: global solutions and absorbing sets. Zbl 1120.35045
Stein, O.; Winkler, M.
2005
Well-posedness and qualitative properties of a dynamical model for the ideal free distribution. Zbl 1317.35116
Cosner, Chris; Winkler, Michael
2014
Chemotactic cross-diffusion in complex frameworks. Zbl 06646361
Winkler, M.
2016
Global weak solutions to a strongly degenerate haptotaxis model. Zbl 1390.35164
Winkler, Michael; Surulescu, Christina
2017
The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
2019
Convergence to a singular steady state of a parabolic equation with gradient blow-up. Zbl 1125.35367
Fila, Marek; Taskinen, Jari; Winkler, Michael
2007
Slow convergence to zero for a parabolic equation with a supercritical nonlinearity. Zbl 1263.35138
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2008
Reduction of critical mass in a chemotaxis system by external application of chemoattractant. Zbl 1295.35136
Tello, José Ignacio; Winkler, Michael
2013
Anisotropic diffusion in oriented environments can lead to singularity formation. Zbl 1273.35165
Hillen, Thomas; Painter, Kevin J.; Winkler, Michael
2013
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
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
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
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
Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation. Zbl 1468.35220
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
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
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
Facing low regularity in chemotaxis systems. Zbl 1436.92004
Lankeit, Johannes; 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
Mathematical analysis of two competing cancer cell migration mechanisms driven by interstitial fluid flow. Zbl 1442.35469
Evje, Steinar; Winkler, Michael
2020
Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065
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
Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250
Li, Genglin; Tao, Youshan; 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
Refined regularity and stabilization properties in a degenerate haptotaxis system. Zbl 1437.35434
Winkler, Michael; Stinner, Christian
2020
Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system. Zbl 1459.92019
Winkler, Michael
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
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
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
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $${n\geq 3}$$. Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
2019
The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
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
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 in a chemotaxis-May-Nowak model for virus dynamics with mildly saturated chemotactic sensitivity. Zbl 1423.35172
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
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
Boundedness and stabilization in a population model with cross-diffusion for one species. Zbl 1439.35275
Tao, Youshan; Winkler, Michael
2019
Migration-driven benefit in a two-species nutrient taxis system. Zbl 1425.92033
Krzyżanowski, Piotr; Winkler, Michael; Wrzosek, Dariusz
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
Singular structure formation in a degenerate haptotaxis model involving myopic diffusion. Zbl 1391.35065
Winkler, Michael
2018
Stabilization in the logarithmic Keller-Segel system. Zbl 1391.35066
Winkler, Michael; Yokota, Tomomi
2018
Global solvability and explicit bounds for non-local adhesion models. Zbl 1406.35430
Hillen, T.; Painter, K. J.; Winkler, M.
2018
Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains. Zbl 1403.35128
Cao, Xinru; Winkler, Michael
2018
Cross-diffusion models: analytic and multiscale problems. Zbl 1408.35078
Bellomo, N.; Tao, Y.; Winkler, M.
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
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
Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 06761738
Tao, Youshan; 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
Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Zbl 1328.35084
Tao, Youshan; Winkler, Michael
2015
Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion. Zbl 1328.35103
Tao, Youshan; Winkler, Michael
2015
Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities. Zbl 1330.35202
Winkler, Michael
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
2015
Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals. Zbl 1329.35075
Winkler, Michael; Tao, Youshan
2015
Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity. Zbl 1329.35011
Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi
2015
Persistence of mass in a chemotaxis system with logistic source. Zbl 1321.35084
Tao, Youshan; Winkler, Michael
2015
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 for a nonlocal and nonlinear Fokker-Planck equation. Zbl 1325.35227
Dreyer, Wolfgang; Huth, Robert; Mielke, Alexander; Rehberg, Joachim; Winkler, Michael
2015
Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation. Zbl 1321.35102
Fila, Marek; Winkler, Michael
2015
A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. I: Local existence of solutions. Zbl 1317.35258
Jüngel, Ansgar; Winkler, Michael
2015
A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. II: Finite-time blow-up. Zbl 1331.35163
Jüngel, Ansgar; Winkler, Michael
2015
Stabilization in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1293.35220
Winkler, Michael
2014
Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening. Zbl 1293.35048
Winkler, Michael
2014
How far can chemotactic cross-diffusion enforce exceeding carrying capacities? Zbl 1311.35040
Winkler, Michael
2014
Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion. Zbl 1301.35189
Stinner, Christian; Surulescu, Christina; Winkler, Michael
2014
Competitive exclusion in a two-species chemotaxis model. Zbl 1319.92050
Stinner, C.; Tello, J. I.; Winkler, M.
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
2014
Dominance of chemotaxis in a chemotaxis-haptotaxis model. Zbl 1293.35047
Tao, Youshan; Winkler, Michael
2014
Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model. Zbl 1312.35171
Tao, Youshan; Winkler, Michael
2014
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
Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. Zbl 1295.35098
Lou, Yuan; Tao, Youshan; Winkler, Michael
2014
Well-posedness and qualitative properties of a dynamical model for the ideal free distribution. Zbl 1317.35116
Cosner, Chris; Winkler, Michael
2014
Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent. Zbl 1295.35085
Fila, M.; King, J. R.; Winkler, M.
2014
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. Zbl 1326.35053
Winkler, Michael
2013
...and 73 more Documents
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#### Cited by 1,090 Authors

 132 Winkler, Michael 64 Mu, Chunlai 45 Tao, Youshan 32 Zheng, Sining 30 Zheng, Pan 28 Wang, Liangchen 28 Zheng, Jiashan 26 Wang, Yifu 25 Lankeit, Johannes 24 Wang, Zhian 24 Yokota, Tomomi 22 Lin, Ke 20 Jin, Hai-Yang 19 Xiang, Zhaoyin 18 Fila, Marek 18 Wang, Wei 17 Shen, Wenxian 17 Viglialoro, Giuseppe 17 Xiang, Tian 16 Fujie, Kentarou 16 Stinner, Christian 15 Hu, Xuegang 15 Mizukami, Masaaki 15 Negreanu, Mihaela 15 Ren, Guoqiang 14 Kang, Kyungkeun 14 Wang, Yulan 13 Black, Tobias 13 Cao, Xinru 13 Liu, Ji 13 Tello, José Ignacio 13 Wang, Yilong 13 Yanagida, Eiji 12 Bellomo, Nicola 12 Li, Xie 12 Surulescu, Christina 12 Yin, Jingxue 12 Zhang, Qingshan 11 Li, Yuxiang 11 Painter, Kevin J. 11 Salako, Rachidi Bolaji 10 Cieślak, Tomasz 10 Guo, Shangjiang 10 Hillen, Thomas 10 Jin, Chunhua 10 Zhang, Qian 9 Fu, Shengmao 9 Ishida, Sachiko 9 Li, Dan 9 Liu, Chein-Shan 9 Morales-Rodrigo, Cristian 8 Jiang, Jie 8 Lee, Jihoon 8 Qiu, Shuyan 8 Shangerganesh, Lingeshwaran 8 Souplet, Philippe 8 Tu, Xinyu 7 Hui, Kin Ming 7 Laurençot, Philippe 7 Liu, Zhengrong 7 Liu, Zuhan 7 Shi, Junping 7 Villamizar-Roa, Elder Jesús 7 Yu, Hao 7 Zhao, Jie 7 Zhigun, Anna 7 Zhou, Shuangshuang 6 Ahn, Jaewook 6 Baghaei, Khadijeh 6 Ding, Mengyao 6 Elaiw, Ahmed M. 6 Fuest, Mario 6 Issa, Tahir Bachar 6 Jüngel, Ansgar 6 Ke, Yuanyuan 6 Li, Jing 6 Ma, Manjun 6 Pan, Xu 6 Suárez, Antonio 6 Vargas, Antonio Manuel 6 Wang, Liangwei 6 Yoon, Changwook 6 Zhang, Zhengce 6 Zhao, Kun 6 Zhao, Xiaopeng 6 Zhou, Ling 6 Zhou, Mingjun 5 Blömker, Dirk 5 Carrillo de la Plata, José Antonio 5 Chae, Myeongju 5 Chaplain, Mark A. J. 5 Chouhad, Nadia 5 Diaz Diaz, Jesus Ildefonso 5 Li, Yuhuan 5 Lv, Wenbin 5 Marras, Monica 5 Mizoguchi, Noriko 5 Osaki, Koichi 5 Pang, Peter Y. H. 5 Peng, Yingping ...and 990 more Authors
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#### Cited in 167 Serials

 155 Journal of Differential Equations 136 Journal of Mathematical Analysis and Applications 72 Nonlinear Analysis. Real World Applications 65 ZAMP. Zeitschrift für angewandte Mathematik und Physik 64 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 62 Discrete and Continuous Dynamical Systems. Series B 54 Discrete and Continuous Dynamical Systems 53 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 39 Applied Mathematics Letters 33 Computers & Mathematics with Applications 30 Mathematical Methods in the Applied Sciences 25 SIAM Journal on Mathematical Analysis 22 Acta Applicandae Mathematicae 20 Nonlinearity 18 Applicable Analysis 18 Discrete and Continuous Dynamical Systems. Series S 17 Journal of Mathematical Physics 15 Calculus of Variations and Partial Differential Equations 15 Communications on Pure and Applied Analysis 14 Journal of Mathematical Biology 13 Boundary Value Problems 12 Journal of Dynamics and Differential Equations 12 NoDEA. Nonlinear Differential Equations and Applications 12 Journal of Evolution Equations 11 Communications in Partial Differential Equations 11 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 Journal of Functional Analysis 9 Mathematische Annalen 9 SIAM Journal on Applied Mathematics 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Journal of Theoretical Biology 7 Applied Mathematics and Computation 7 Mathematical Biosciences and Engineering 6 Proceedings of the American Mathematical Society 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Discrete Dynamics in Nature and Society 6 Journal of Mathematical Fluid Mechanics 6 Kinetic and Related Models 6 Advances in Nonlinear Analysis 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Physica D 5 European Journal of Applied Mathematics 5 Advances in Difference Equations 4 Archive for Rational Mechanics and Analysis 4 Transactions of the American Mathematical Society 4 Journal of Scientific Computing 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Journal of Nonlinear Science 4 Electronic Journal of Differential Equations (EJDE) 4 Advanced Nonlinear Studies 4 International Journal of Biomathematics 4 Science China. Mathematics 3 Journal d’Analyse Mathématique 3 Applied Mathematics and Optimization 3 Mathematische Nachrichten 3 Results in Mathematics 3 Applied Mathematics. Series B (English Edition) 3 Abstract and Applied Analysis 3 Journal of Dynamical and Control Systems 2 Communications in Mathematical Physics 2 Israel Journal of Mathematics 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Journal of Computational Physics 2 Rocky Mountain Journal of Mathematics 2 Bulletin of Mathematical Biology 2 Archiv der Mathematik 2 Czechoslovak Mathematical Journal 2 Duke Mathematical Journal 2 Funkcialaj Ekvacioj. Serio Internacia 2 Indiana University Mathematics Journal 2 Journal of Computational and Applied Mathematics 2 Monatshefte für Mathematik 2 Numerische Mathematik 2 Osaka Journal of Mathematics 2 Quarterly of Applied Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Japan Journal of Industrial and Applied Mathematics 2 Applied Mathematical Modelling 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Topological Methods in Nonlinear Analysis 2 Engineering Analysis with Boundary Elements 2 Journal of Inequalities and Applications 2 Communications in Nonlinear Science and Numerical Simulation 2 Nonlinear Analysis. Modelling and Control 2 Journal of Applied Mathematics 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Multiscale Modeling & Simulation 2 Analysis and Applications (Singapore) 2 Oberwolfach Reports 2 Journal of Biological Dynamics 1 Lithuanian Mathematical Journal 1 Physica A 1 Advances in Mathematics 1 The Annals of Probability 1 Calcolo 1 Hokkaido Mathematical Journal 1 Journal of the Korean Mathematical Society 1 Journal of the London Mathematical Society. Second Series 1 Manuscripta Mathematica ...and 67 more Serials
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#### Cited in 30 Fields

 1,273 Partial differential equations (35-XX) 933 Biology and other natural sciences (92-XX) 100 Fluid mechanics (76-XX) 61 Numerical analysis (65-XX) 37 Ordinary differential equations (34-XX) 24 Dynamical systems and ergodic theory (37-XX) 19 Statistical mechanics, structure of matter (82-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 15 Probability theory and stochastic processes (60-XX) 10 Operator theory (47-XX) 10 Mechanics of deformable solids (74-XX) 9 Systems theory; control (93-XX) 8 Integral equations (45-XX) 6 Real functions (26-XX) 6 Functional analysis (46-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Differential geometry (53-XX) 3 General and overarching topics; collections (00-XX) 3 Potential theory (31-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX)