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Author ID: winkler.michael Recent zbMATH articles by "Winkler, Michael"
Published as: Winkler, Michael; Winkler, M.
Homepage: https://www2.math.uni-paderborn.de/?id=16819
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Serials

23 Journal of Differential Equations
15 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
11 Nonlinearity
11 SIAM Journal on Mathematical Analysis
9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
8 Mathematical Methods in the Applied Sciences
8 ZAMP. Zeitschrift für angewandte Mathematik und Physik
8 Communications in Partial Differential Equations
7 Discrete and Continuous Dynamical Systems
6 European Journal of Applied Mathematics
6 Journal of Dynamics and Differential Equations
6 Advances in Differential Equations
6 Nonlinear Analysis. Real World Applications
5 Journal of Mathematical Analysis and Applications
5 Indiana University Mathematics Journal
5 Mathematische Annalen
5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
5 NoDEA. Nonlinear Differential Equations and Applications
5 Journal of Evolution Equations
4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
4 Calculus of Variations and Partial Differential 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 Journal of the London Mathematical Society. Second Series
3 Mathematische Nachrichten
3 Journal de Mathématiques Pures et Appliquées. Neuvième Série
3 Journal of the European Mathematical Society (JEMS)
3 Advanced Nonlinear Studies
3 Communications in Mathematical Sciences
3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
2 Communications in Mathematical Physics
2 Israel Journal of Mathematics
2 Applied Mathematics and Optimization
2 Journal of Functional Analysis
2 Proceedings of the London Mathematical Society. Third Series
2 Transactions of the American Mathematical Society
2 Acta Applicandae Mathematicae
2 Applied Mathematics Letters
2 Asymptotic Analysis
2 IMRN. International Mathematics Research Notices
2 SIAM Journal on Applied Mathematics
2 Journal of Nonlinear Science
2 Advances in Nonlinear Analysis
1 Applicable 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 Rendiconti dell’Istituto di Matematica dell’Università di Trieste
1 Studies in Applied Mathematics
1 Zeitschrift für Analysis und ihre Anwendungen
1 Acta Mathematica Universitatis Comenianae. New Series
1 INFORMS Journal on Computing
1 Journal of Mathematical Fluid Mechanics
1 Acta Mathematica Sinica. English Series
1 Communications in Contemporary Mathematics
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 Bulletin of Mathematical Sciences
1 Evolution Equations and Control Theory
1 Open Mathematics
1 Journal of Elliptic and Parabolic Equations
1 Transactions of the American Mathematical Society. Series B
1 SN Partial Differential Equations and Applications
1 OJMO. Open Journal of Mathematical Optimization

Publications by Year

Citations contained in zbMATH Open

236 Publications have been cited 14,363 times in 2,380 Documents Cited by Year
Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model. Zbl 1190.92004
Winkler, Michael
842
2010
Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Zbl 1326.35397
Bellomo, N.; Bellouquid, A.; Tao, Y.; Winkler, M.
688
2015
Boundedness vs. blow-up in a chemotaxis system. Zbl 1085.35065
Horstmann, Dirk; Winkler, Michael
652
2005
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. Zbl 1326.35053
Winkler, Michael
643
2013
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity. Zbl 1382.35127
Tao, Youshan; Winkler, Michael
542
2012
Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source. Zbl 1290.35139
Winkler, Michael
528
2010
Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Zbl 1236.35192
Winkler, Michael
443
2012
A chemotaxis system with logistic source. Zbl 1121.37068
Tello, J. Ignacio; Winkler, Michael
419
2007
Stabilization in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1293.35220
Winkler, Michael
311
2014
Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Zbl 1351.35239
Winkler, Michael
250
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
249
2012
Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction. Zbl 1241.35028
Winkler, Michael
235
2011
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Zbl 1345.35117
Bai, Xueli; Winkler, Michael
234
2016
Does a volume-filling effect always prevent chemotactic collapse? Zbl 1182.35220
Winkler, Michael
229
2010
Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening. Zbl 1293.35048
Winkler, Michael
226
2014
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity. Zbl 1333.35104
Winkler, Michael
196
2015
Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect. Zbl 1183.92012
Winkler, Michael; Djie, Kianhwa C.
192
2010
Finite-time blow-up in a quasilinear system of chemotaxis. Zbl 1136.92006
Cieślak, Tomasz; Winkler, Michael
190
2008
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Zbl 1356.35071
Winkler, Michael
190
2017
Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion. Zbl 1301.35189
Stinner, Christian; Surulescu, Christina; Winkler, Michael
188
2014
Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Zbl 1283.35154
Tao, Youshan; Winkler, Michael
179
2013
Chemotaxis with logistic source: very weak global solutions and their boundedness properties. Zbl 1147.92005
Winkler, Michael
173
2008
Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Zbl 1328.35084
Tao, Youshan; Winkler, Michael
166
2015
A chemotaxis-haptotaxis model: the roles of nonlinear diffusion and logistic source. Zbl 1259.35210
Tao, Youshan; Winkler, Michael
162
2011
How far can chemotactic cross-diffusion enforce exceeding carrying capacities? Zbl 1311.35040
Winkler, Michael
162
2014
Global solutions in a fully parabolic chemotaxis system with singular sensitivity. Zbl 1291.92018
Winkler, Michael
161
2011
Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Zbl 1276.35105
Tao, Youshan; Winkler, Michael
154
2012
Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048
Winkler, Michael
153
2018
Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion. Zbl 1328.35103
Tao, Youshan; Winkler, Michael
141
2015
Stabilization in a two-species chemotaxis system with a logistic source. Zbl 1260.92014
Tello, J. I.; Winkler, M.
139
2012
Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity. Zbl 1205.35037
Winkler, Michael
136
2010
Competitive exclusion in a two-species chemotaxis model. Zbl 1319.92050
Stinner, C.; Tello, J. I.; Winkler, M.
133
2014
Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities. Zbl 1330.35202
Winkler, Michael
132
2015
A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. Zbl 1408.35132
Winkler, Michael
132
2019
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
125
2014
Stabilization in a chemotaxis model for tumor invasion. Zbl 1322.35059
Yokota, Tomomi; Winkler, Michael; Ito, Akio; Fujie, Kentarou
124
2016
Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Zbl 1356.35054
Tao, Youshan; Winkler, Michael
119
2016
Global weak solutions in a chemotaxis system with large singular sensitivity. Zbl 1268.35072
Stinner, Christian; Winkler, Michael
100
2011
Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 1516.35092
Tao, Youshan; Winkler, Michael
100
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
98
2017
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068
Tao, Youshan; Winkler, Michael
98
2017
A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240
Winkler, Michael
95
2018
The two-dimensional Keller-Segel system with singular sensitivity and signal absorption: global large-data solutions and their relaxation properties. Zbl 1383.35099
Winkler, Michael
92
2016
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
91
2018
Convergence of a cancer invasion model to a logistic chemotaxis model. Zbl 1263.35204
Hillen, Thomas; Painter, Kevin J.; Winkler, Michael
89
2013
Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals. Zbl 1329.35075
Winkler, Michael; Tao, Youshan
86
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
84
2015
A fourth-order parabolic equation modeling epitaxial thin film growth. Zbl 1029.35110
King, Belinda B.; Stein, Oliver; Winkler, Michael
82
2003
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Zbl 1395.35038
Winkler, Michael
72
2018
A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166
Bellomo, Nicola; Winkler, Michael
68
2017
Blow-up prevention by logistic sources in a parabolic-elliptic Keller-Segel system with singular sensitivity. Zbl 1297.35051
Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi
67
2014
Dominance of chemotaxis in a chemotaxis-haptotaxis model. Zbl 1293.35047
Tao, Youshan; Winkler, Michael
67
2014
A critical exponent in a degenerate parabolic equation. Zbl 1007.35043
Winkler, Michael
67
2002
Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity. Zbl 1329.35011
Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi
66
2015
Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems. Zbl 1377.35158
Winkler, Michael
66
2017
Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation. Zbl 1370.35059
Winkler, Michael
64
2017
Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044
Bellomo, Nicola; Winkler, Michael
64
2017
Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model. Zbl 1312.35171
Tao, Youshan; Winkler, Michael
64
2014
Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations. Zbl 1441.35079
Winkler, Michael
63
2020
Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption. Zbl 1378.35165
Winkler, Michael
61
2018
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
59
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
56
2020
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Zbl 1404.35464
Winkler, Michael
56
2018
Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity? Zbl 1409.35047
Winkler, Michael
56
2018
Persistence of mass in a chemotaxis system with logistic source. Zbl 1321.35084
Tao, Youshan; Winkler, Michael
53
2015
Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. Zbl 1497.35039
Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M.
52
2022
Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems? Zbl 1483.35294
Winkler, Michael
52
2021
Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization. Zbl 1392.35042
Espejo, Elio; Winkler, Michael
52
2018
Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052
Winkler, Michael
48
2019
Facing low regularity in chemotaxis systems. Zbl 1436.92004
Lankeit, Johannes; Winkler, Michael
47
2020
The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system. Zbl 1397.35322
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
44
2018
Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065
Winkler, Michael
43
2020
Stabilization in the logarithmic Keller-Segel system. Zbl 1391.35066
Winkler, Michael; Yokota, Tomomi
40
2018
Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food. Zbl 1425.35200
Tao, Youshan; Winkler, Michael
39
2019
Global regularity versus infinite-time singularity formation in a chemotaxis model with volume-filling effect and degenerate diffusion. Zbl 1277.35223
Wang, Zhi-An; Winkler, Michael; Wrzosek, Dariusz
39
2012
Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132
Tao, Youshan; Winkler, Michael
39
2020
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
38
2019
Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612
Winkler, Michael
38
2019
Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity. Zbl 1382.35048
Winkler, Michael
38
2017
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
34
2021
Global existence and uniform boundedness of smooth solutions to a cross-diffusion system with equal diffusion rates. Zbl 1332.35172
Lou, Yuan; Winkler, Michael
34
2015
A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480
Tao, Youshan; Winkler, Michael
34
2020
Singular structure formation in a degenerate haptotaxis model involving myopic diffusion. Zbl 1391.35065
Winkler, Michael
33
2018
\(L^1\) solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation. Zbl 1517.35096
Winkler, Michael
33
2023
Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Zbl 1428.35611
Winkler, Michael
32
2019
Global bounded solutions in a two-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1364.35124
Cieślak, Tomasz; Winkler, Michael
32
2017
Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity. Zbl 1367.35033
Cieślak, Tomasz; Winkler, Michael
30
2017
How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases. Zbl 1416.35049
Winkler, Michael
28
2019
Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation. Zbl 1460.35358
Winkler, Michael
28
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
28
2021
Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250
Li, Genglin; Tao, Youshan; Winkler, Michael
26
2020
The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
26
2019
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
25
2021
Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Zbl 1518.35109
Li, Genglin; Winkler, Michael
25
2023
Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system. Zbl 1459.92019
Winkler, Michael
24
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
24
2020
A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181
Tao, Youshan; Winkler, Michael
23
2019
Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Zbl 1458.35076
Tao, Youshan; Winkler, Michael
23
2021
Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. Zbl 1466.35060
Winkler, Michael
23
2021
Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. Zbl 1295.35098
Lou, Yuan; Tao, Youshan; Winkler, Michael
23
2014
A quantitative strong parabolic maximum principle and application to a taxis-type migration-consumption model involving signal-dependent degenerate diffusion. Zbl 07822734
Winkler, Michael
4
2024
Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. Zbl 07859113
Li, Genglin; Winkler, Michael
2
2024
Approaching critical decay in a strongly degenerate parabolic equation. Zbl 1536.35080
Winkler, Michael
1
2024
\(L^1\) solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation. Zbl 1517.35096
Winkler, Michael
33
2023
Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Zbl 1518.35109
Li, Genglin; Winkler, Michael
25
2023
Does Leray’s structure theorem withstand buoyancy-driven chemotaxis-fluid interaction? Zbl 1520.35027
Winkler, Michael
16
2023
Application of the Moser-Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. Zbl 07735866
Winkler, Michael
14
2023
Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Zbl 1505.35340
Tao, Youshan; Winkler, Michael
14
2023
Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. Zbl 1501.35057
Desvillettes, Laurent; Laurençot, Philippe; Trescases, Ariane; Winkler, Michael
14
2023
Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration-consumption interaction. Zbl 1504.35181
Winkler, Michael
11
2023
Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration-consumption interaction. Zbl 1525.35040
Winkler, Michael
7
2023
Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Zbl 1525.35038
Tao, Youshan; Winkler, Michael
6
2023
Finite-time blow-up in a repulsive chemotaxis-consumption system. Zbl 1518.35155
Wang, Yulan; Winkler, Michael
4
2023
Adaptive cut selection in mixed-integer linear programming. Zbl 1522.90045
Turner, Mark; Koch, Thorsten; Serrano, Felipe; Winkler, Michael
3
2023
A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. Zbl 1521.35053
Ahn, Jaewook; Winkler, Michael
3
2023
Classical solutions to Cauchy problems for parabolic-elliptic systems of Keller-Segel type. Zbl 1523.35268
Winkler, Michael
3
2023
Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Zbl 1518.35439
Tao, Youshan; Winkler, Michael
2
2023
A result on parabolic gradient regularity in Orlicz spaces and application to absorption-induced blow-up prevention in a Keller-Segel-type cross-diffusion system. Zbl 1532.35107
Winkler, Michael
2
2023
Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. Zbl 1520.35157
Winkler, Michael
1
2023
Exponential grow-up rates in a quasilinear Keller-Segel system. Zbl 1509.35325
Winkler, Michael
1
2023
Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. Zbl 1523.35083
Tao, Youshan; Winkler, Michael
1
2023
Keller-Segel-Stokes interaction involving signal-dependent motilities. Zbl 1531.35127
Tian, Yu; Winkler, Michael
1
2023
Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. Zbl 1497.35039
Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M.
52
2022
Reaction-driven relaxation in three-dimensional Keller-Segel-Navier-Stokes interaction. Zbl 1486.35102
Winkler, Michael
22
2022
Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system. Zbl 1496.35228
Tao, Youshan; Winkler, Michael
18
2022
A critical blow-up exponent for flux limiation in a Keller-Segel system. Zbl 1501.35094
Winkler, Michael
18
2022
Unlimited growth in logarithmic Keller-Segel systems. Zbl 1480.35383
Winkler, Michael
16
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
13
2022
Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy. Zbl 1484.35363
Tao, Youshan; Winkler, Michael
12
2022
Global weak solutions and absorbing sets in a chemotaxis-Navier-Stokes system with prescribed signal concentration on the boundary. Zbl 1487.35372
Black, Tobias; Winkler, Michael
12
2022
A unifying approach toward boundedness in Keller-Segel type cross-diffusion systems via conditional \(L^{\infty}\) estimates for taxis gradients. Zbl 1525.35050
Winkler, Michael
11
2022
Chemotaxis-Stokes interaction with very weak diffusion enhancement: blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings. Zbl 1511.35053
Winkler, Michael
11
2022
A family of mass-critical Keller-Segel systems. Zbl 1522.35524
Winkler, Michael
10
2022
Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities. Zbl 1503.35051
Winkler, Michael
10
2022
On the global existence and qualitative behaviour of one-dimensional solutions to a model for urban crime. Zbl 1503.35234
Rodriguez, Nancy; Winkler, Michael
10
2022
Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary. Zbl 1481.35023
Lankeit, Johannes; Winkler, Michael
8
2022
Nonnegative solutions to a doubly degenerate nutrient taxis system. Zbl 1483.35127
Li, Genglin; Winkler, Michael
8
2022
Small-signal solutions of a two-dimensional doubly degenerate taxis system modeling bacterial motion in nutrient-poor environments. Zbl 1479.35224
Winkler, Michael
8
2022
A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system. Zbl 1494.35047
Fuhrmann, Jan; Lankeit, Johannes; Winkler, Michael
7
2022
A smallness condition ensuring boundedness in a two-dimensional chemotaxis-Navier-Stokes system involving Dirichlet boundary conditions for the signal. Zbl 1491.92033
Wang, Yu Lan; Winkler, Michael; Xiang, Zhao Yin
6
2022
Global weak solutions to a chemotaxis-Navier-Stokes system in \(\mathbb{R}^3 \). Zbl 1498.92032
Kang, Kyungkeun; Lee, Jihoon; Winkler, Michael
5
2022
Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects. Zbl 1485.35266
Lankeit, Johannes; Winkler, Michael
1
2022
Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar. Zbl 1491.35055
Winkler, Michael
1
2022
Taxis-driven persistent localization in a degenerate Keller-Segel system. Zbl 1505.35045
Stevens, Angela; Winkler, Michael
1
2022
Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems? Zbl 1483.35294
Winkler, Michael
52
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
34
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
28
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
28
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
25
2021
Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Zbl 1458.35076
Tao, Youshan; Winkler, Michael
23
2021
Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. Zbl 1466.35060
Winkler, Michael
23
2021
Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. Zbl 1479.35120
Tao, Youshan; Winkler, Michael
22
2021
Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation. Zbl 1468.35220
Winkler, Michael
18
2021
Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity. Zbl 1453.35115
Winkler, Michael
16
2021
Taxis-driven formation of singular hotspots in a May-Nowak-type model for virus infection. Zbl 1461.35201
Tao, Youshan; Winkler, Michael
15
2021
A critical virus production rate for efficiency of oncolytic virotherapy. Zbl 1526.92012
Tao, Youshan; Winkler, Michael
14
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
11
2021
Small-density solutions in Keller-Segel systems involving rapidly decaying diffusivities. Zbl 1471.35064
Ding, Mengyao; Winkler, Michael
10
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
9
2021
Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis-haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more). Zbl 1503.35243
Surulescu, Christina; Winkler, Michael
4
2021
The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. Zbl 1465.35378
Tao, Youshan; Winkler, Michael
2
2021
Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations. Zbl 1441.35079
Winkler, Michael
63
2020
The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in \(L^{1}\). Zbl 1419.35099
Winkler, Michael
56
2020
Facing low regularity in chemotaxis systems. Zbl 1436.92004
Lankeit, Johannes; Winkler, Michael
47
2020
Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions. Zbl 1465.35065
Winkler, Michael
43
2020
Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132
Tao, Youshan; Winkler, Michael
39
2020
A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480
Tao, Youshan; Winkler, Michael
34
2020
Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250
Li, Genglin; Tao, Youshan; Winkler, Michael
26
2020
Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system. Zbl 1459.92019
Winkler, Michael
24
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
24
2020
Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation. Zbl 1451.35226
Rodríguez, Nancy; Winkler, Michael
16
2020
Single-point blow-up in the Cauchy problem for the higher-dimensional Keller-Segel system. Zbl 1452.35227
Winkler, Michael
10
2020
Mathematical analysis of two competing cancer cell migration mechanisms driven by interstitial fluid flow. Zbl 1442.35469
Evje, Steinar; Winkler, Michael
8
2020
Boundedness in a two-dimensional Keller-Segel-Navier-Stokes system involving a rapidly diffusing repulsive signal. Zbl 1432.92021
Winkler, Michael
7
2020
Chemotaxis systems in complex frameworks: pattern formation, qualitative analysis and blowup prevention. Zbl 1451.92062
Bellomo, N.; Tao, Y.; Winkler, M.
6
2020
Refined regularity and stabilization properties in a degenerate haptotaxis system. Zbl 1437.35434
Winkler, Michael; Stinner, Christian
5
2020
Can fluid interaction influence the critical mass for taxis-driven blow-up in bounded planar domains? Zbl 1464.35046
Winkler, Michael
4
2020
A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. Zbl 1408.35132
Winkler, Michael
132
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
59
2019
Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities. Zbl 1415.35052
Winkler, Michael
48
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
39
2019
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions \({n\geq 3}\). Zbl 1411.35140
Souplet, Philippe; Winkler, Michael
38
2019
Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Zbl 1428.35612
Winkler, Michael
38
2019
Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Zbl 1428.35611
Winkler, Michael
32
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
28
2019
The fast signal diffusion limit in Keller-Segel(-fluid) systems. Zbl 1426.92009
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
26
2019
A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181
Tao, Youshan; Winkler, Michael
23
2019
Boundedness in a chemotaxis-May-Nowak model for virus dynamics with mildly saturated chemotactic sensitivity. Zbl 1423.35172
Winkler, Michael
23
2019
Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension. Zbl 1411.35146
Tao, Youshan; Winkler, Michael
21
2019
How strong singularities can be regularized by logistic degradation in the Keller-Segel system? Zbl 1437.35004
Winkler, Michael
16
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
13
2019
Boundedness and stabilization in a population model with cross-diffusion for one species. Zbl 1439.35275
Tao, Youshan; Winkler, Michael
10
2019
A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation. Zbl 1428.26026
Fila, Marek; Winkler, Michael
6
2019
Instantaneous regularization of distributions from \((C^0)^\star \times L^2\) in the one-dimensional parabolic Keller-Segel system. Zbl 1428.35632
Winkler, Michael
5
2019
Structure-driven fix-and-propagate heuristics for mixed integer programming. Zbl 1432.90091
Gamrath, Gerald; Berthold, Timo; Heinz, Stefan; Winkler, Michael
5
2019
Migration-driven benefit in a two-species nutrient taxis system. Zbl 1425.92033
Krzyżanowski, Piotr; Winkler, Michael; Wrzosek, Dariusz
3
2019
Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal degenerate parabolic equation arising in game theory. Zbl 1433.35181
Lankeit, Johannes; Winkler, Michael
1
2019
Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation. Zbl 1395.35048
Winkler, Michael
153
2018
A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Zbl 1391.35240
Winkler, Michael
95
2018
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Zbl 1395.92024
Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin
91
2018
...and 136 more Documents
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Cited by 1,885 Authors

191 Winkler, Michael
83 Mu, Chunlai
59 Tao, Youshan
54 Zheng, Jiashan
53 Zheng, Pan
45 Wang, Liangchen
43 Yokota, Tomomi
42 Liu, Bin
39 Wang, Zhian
38 Lankeit, Johannes
38 Ren, Guoqiang
35 Zheng, Sining
33 Wang, Yifu
30 Xiang, Zhaoyin
27 Jin, Haiyang
26 Mizukami, Masaaki
26 Viglialoro, Giuseppe
25 Lin, Ke
24 Kang, Kyungkeun
24 Shen, Wenxian
23 Wang, Wei
23 Xiang, Tian
22 Fujie, Kentaro
22 Wang, Qi
21 Fila, Marek
21 Liu, Zuhan
20 Liu, Ji
19 Fuest, Mario
19 Negreanu, Mihaela
19 Yin, Jingxue
18 Hu, Xuegang
18 Liu, Changchun
18 Stinner, Christian
18 Wang, Yulan
18 Zhang, Qingshan
17 Black, Tobias
17 Elaiw, Ahmed M.
17 Jin, Chunhua
17 Qiu, Shuyan
17 Surulescu, Christina
17 Zhang, Qian
17 Zhou, Ling
16 Cao, Xinru
16 Dai, Feng
16 Jiang, Jie
16 Tello, José Ignacio
15 Bellomo, Nicola
15 Guillén González, Francisco M.
15 Guo, Shangjiang
15 Li, Zhongping
15 Painter, Kevin J.
15 Tu, Xinyu
14 Ke, Yuanyuan
14 Wang, Jianping
14 Yanagida, Eiji
13 Cieślak, Tomasz
13 Laurençot, Philippe
13 Li, Dan
13 Pan, Xu
13 Salako, Rachidi Bolaji
13 Wang, Yilong
13 Zhao, Jie
12 Hillen, Thomas
12 Ishida, Sachiko
12 Lee, Jihoon
12 Li, Xie
12 Li, Yuxiang
12 Yoon, Changwook
11 Ahn, Jaewook
11 Li, Jing
11 Lyu, Wenbin
11 Rueda-Gómez, Diego Armando
11 Shangerganesh, Lingeshwaran
11 Souplet, Philippe
11 Villamizar-Roa, Elder Jesús
10 Baghaei, Khadijeh
10 Chiyo, Yutaro
10 Fu, Shengmao
10 Marras, Monica
10 Vargas, Antonio Manuel
10 Wang, Mingxin
10 Zhao, Xiangdong
10 Zhigun, Anna
10 Zhou, Jun
9 Ding, Mengyao
9 Frassu, Silvia
9 Li, Bin
9 Li, Yan
9 Liu, Zhengrong
9 Morales-Rodrigo, Cristian
9 Shi, Junping
9 Tanaka, Yuya
9 Vernier-Piro, Stella
9 Wang, Liangwei
9 Wu, Sainan
9 Xie, Li
9 Xing, Jie
9 Xu, Lu
9 Zhang, Wenji
8 Alshamrani, Noura H.
...and 1,785 more Authors
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Cited in 243 Serials

235 Journal of Differential Equations
187 Journal of Mathematical Analysis and Applications
131 Discrete and Continuous Dynamical Systems. Series B
125 Nonlinear Analysis. Real World Applications
119 ZAMP. Zeitschrift für angewandte Mathematik und Physik
107 Mathematical Methods in the Applied Sciences
97 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
70 Discrete and Continuous Dynamical Systems
69 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
63 Applied Mathematics Letters
42 Nonlinearity
40 Acta Applicandae Mathematicae
37 Computers & Mathematics with Applications
35 SIAM Journal on Mathematical Analysis
33 Applicable Analysis
31 Communications on Pure and Applied Analysis
31 Discrete and Continuous Dynamical Systems. Series S
30 Boundary Value Problems
28 Journal of Mathematical Physics
28 Calculus of Variations and Partial Differential Equations
21 Journal of Mathematical Biology
21 Journal of Evolution Equations
20 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
20 Journal of Dynamics and Differential Equations
19 NoDEA. Nonlinear Differential Equations and Applications
17 Mathematische Nachrichten
15 Journal of Functional Analysis
15 Mathematical Biosciences and Engineering
14 Communications in Partial Differential Equations
13 Electronic Research Archive
12 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
12 European Journal of Applied Mathematics
12 SIAM Journal on Applied Mathematics
12 Journal of Nonlinear Science
12 Communications in Nonlinear Science and Numerical Simulation
11 Comptes Rendus. Mathématique. Académie des Sciences, Paris
10 Applied Mathematics and Computation
10 Applied Mathematics and Optimization
10 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
10 Journal of Mathematical Fluid Mechanics
10 Journal of Theoretical Biology
10 Advances in Nonlinear Analysis
9 Mathematische Annalen
9 Studies in Applied Mathematics
9 Physica D
9 Journal de Mathématiques Pures et Appliquées. Neuvième Série
9 Electronic Journal of Differential Equations (EJDE)
9 Acta Mathematica Scientia. Series B. (English Edition)
9 International Journal of Biomathematics
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8 Advances in Difference Equations
7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
7 Advanced Nonlinear Studies
7 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
6 Archive for Rational Mechanics and Analysis
6 Journal of Computational Physics
6 Annali di Matematica Pura ed Applicata. Serie Quarta
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5 Journal of Computational and Applied Mathematics
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5 Acta Mathematica Sinica. English Series
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5 Mathematical Programming Computation
4 Communications in Mathematical Physics
4 Computer Methods in Applied Mechanics and Engineering
4 Physica A
4 Chaos, Solitons and Fractals
4 Bulletin of the London Mathematical Society
4 Indiana University Mathematics Journal
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4 Japan Journal of Industrial and Applied Mathematics
4 Journal of Inequalities and Applications
4 Journal of Dynamical and Control Systems
4 Communications in Contemporary Mathematics
4 Qualitative Theory of Dynamical Systems
4 SIAM Journal on Applied Dynamical Systems
4 Analysis and Applications (Singapore)
4 Open Mathematics
4 Mathematics in Engineering
3 Journal d’Analyse Mathématique
3 Archiv der Mathematik
3 Czechoslovak Mathematical Journal
3 Monatshefte für Mathematik
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3 Computers & Operations Research
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3 Abstract and Applied Analysis
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