2017

Bellomo, N., Winkler, M.:
 A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up.
 Erscheint in: Communications in Partial Differential Equations   <Preprint>

Bellomo, N., Winkler, M.:
  Finite-time blow-up in a degenerate chemotaxis system with flux limitation.
 Erscheint in: Transactions of the American Mathematical Society   < Preprint>

Cao, X., Winkler, M.:
 Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains.
 Erscheint in: Proceedings of the Royal Society of Edinburgh: Section A   <Preprint>

Cieślak, T., Winkler, M.:
 Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity.
 Erscheint in: Nonlinear Analysis (Special Issue).   <Preprint>

Fila, M., Winkler, M.:
 Slow growth of solutions of super-fast diffusion equations with unbounded initial data.
 Erscheint in: Journal of the London Mathematical Society   <Preprint>

Kavallaris, N. Lankeit, J., Winkler, M.:
 On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics.
 Erscheint in: SIAM Journal on Mathematical Analysis   <Preprint>

Lou, Y., Tao, Y., Winkler, M.:
 Nonexistence of Nonconstant Steady-State Solutions in a Triangular Cross-Diffusion Model.
 Erscheint in: Journal of Differential Equations   <Preprint>

Surulescu, C., Winkler, M.:
  Global weak solutions to a strongly degenerate haptotaxis model.
 Erscheint in: Communications in Mathematical Sciences   <Preprint>

Tao, Y., Winkler, M.:
 Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production.
 Erscheint in: Journal of the European Mathematical Society.   <Preprint>

Tao, Y., Winkler, M.:
 Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system.
 Erscheint in: Mathematical Models and Methods in Applied Sciences   <Preprint>

Wang, Y., Winkler, M., Xiang, Z.:
 Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity.
 Erscheint in: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze   <Preprint>

Winkler, M.:
 One-dimensional super-fast diffusion: Persistence vs.~extinction revisited. Extinction at spatial infinity.
 Erscheint in: Journal of Dynamics and Differential Equations   <Preprint>

Winkler, M.:
  Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity.
 Erscheint in: Nonlinearity   <Preprint>

Winkler, M.:
 Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems.
 Erscheint in: Discrete and Continuous Dynamical Systems - B   <Preprint>

Cieślak, T., Winkler, M.:
  Global bounded solutions in a two-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity.
 Nonlinear Analysis: Real World Applications 35, 1-19 (2017)   <Preprint>

Winkler, M.:
  How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?
 Transactions of the American Mathematical Society 369, 3067-3125 (2017)   <Preprint>

2016

Bai, X., Winkler, M.:
 Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics.
  Indiana University Mathematics Journal 65, 553-583 (2016)   <Preprint>

Fila, M., Winkler, M.:
 Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation.
  Proceedings of the Royal Society of Edinburgh: Section A 146, 309-324 (2016)   <Preprint>

Fila, M., Winkler, M.:
 Rate of convergence to separable solutions of the fast diffusion equation.
  Israel Journal of Mathematics 213, 1-32 (2016) 

Fujie, K., Ito, A., Winkler, M., Yokota, T.:
 Stabilization in a chemotaxis model for tumor invasion.
  Discrete and Continuous Dynamical Systems 36, 151-169 (2016)   <Preprint>

Tao, Y., Winkler, M.:
 Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system.
  Zeitschrift für Angewandte Mathematik und Physik 67, Art. 138, 23 S. (2016)  <Preprint>

Winkler, M.:
  Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system.
  Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 33, 1329-1352 (2016)   <Preprint>

Winkler, M.:
  The two-dimensional Keller-Segel system with singular sensitivity and signal absorption: global large-data solutions and their relaxation properties.
  Mathematical Models and Methods in Applied Sciences 26, 987-1024 (2016)   <Preprint>

2015

Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M.:
  Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues.
  Mathematical Models and Methods in Applied Sciences 25, 1663-1763 (2015) 

Dreyer, W., Huth, R., Mielke, A., Rehberg, J., Winkler, M.:
 Global existence for a nonlocal and nonlinear Fokker-Planck equation.
 Zeitschrift für Angewandte Mathematik und Physik 66, 293-315 (2015) 

Fila, M., Winkler, M.:
 Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation.
 Communications on Pure and Applied Analysis 14, 107-119 (2015)   <Preprint>

Fujie, K., Winkler, M., Yokota, T.:
 Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity.
 Mathematical Methods in the Applied Sciences 38, 1212-1224 (2015) 

Jüngel, A., Winkler, M.:
 A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. Part I: Local existence of solutions.
 Archive for Rational Mechanics and Analysis 217, 935-973 (2015)   <Preprint>

Jüngel, A., Winkler, M.:
 A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. Part II: Finite-time blow-up.
 Communications in Partial Differential Equations 40, 1748-1786 (2015)   <Preprint>

Li, T., Suen, A., Winkler, M., Xue, C.:
 Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms.
 Mathematical Models and Methods in Applied Sciences 25, 721-746 (2015) 

Lou, Y., Winkler, M.:
 Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates.
 Communications in Partial Differential Equations 40, 1905-1941 (2015)   <Preprint>

Tao, Y., Winkler, M.:
 Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion.
 SIAM Journal on Mathematical Analysis 47, 4229-4250 (2015) 

Tao, Y., Winkler, M.:
 Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system.
 Zeitschrift für Angewandte Mathematik und Physik 66, 2555-2573 (2015)   <Preprint>

Tao, Y., Winkler, M.:
 Persistence of mass in a chemotaxis system with logistic source.
 Journal of Differential Equations 259, 6142-6161 (2015)   <Preprint>

Tao, Y., Winkler, M.:
 Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals.
 Discrete and Continuous Dynamical Systems - B 20, 3165-3183 (2015)   <Preprint>

Winkler, M.:
 Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity.
 Calculus of Variations and Partial Differential Equations 54, 3789-3828 (2015)   <Preprint>

Winkler, M.:
 Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities.
 SIAM Journal on Mathematical Analysis 47, 3092-3115 (2015)   <Preprint>

2014

Fila, M., King, J.R., Winkler, M.:
 Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation with a Critical Exponent.
  J. Lond. Math. Soc. (2) 90, no. 1, 167–183 (2014) <Preprint>

Cosner, C., Winkler, M.:
 Well-posedness and qualitative properties of a dynamical model for the ideal free distribution.
 Journal of Mathematical Biology 69 (6-7) 1343-1382 (2014)

Fujie, K., Winkler, M., Yokota, T.:
 Blow-up prevention by logistic sources in a parabolic-elliptic Keller-Segel system with singular sensitivity.
 Nonlinear Analysis, Theory Methods Appl. 109, 56-71 (2014)

Lou, Y., Tao, Y., Winkler, M.:
 Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal.
 SIAM Journal of Mathematical Analysis 46 (2), 1228-1262 (2014)

Stinner, C., Surulescu, C., Winkler, M.:
 Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion.
 SIAM Journal of Mathematical Analysis 46 (3), 1969-2007 (2014)

Stinner, C., Tello, J.I., Winkler, M.:
 Competitive exclusion in a two-species chemotaxis model.
 Journal of Mathematical Biology 68 (7), 1607-1626 (2014)

Tao, Y., Winkler, M.:
 Energy-type estimates and global solvability in a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant.
 Journal of Differential Equations 257 (3), 784-815 (2014)

Tao, Y., Winkler, M.:
 Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model.
 Proceedings of the Royal Society of Edinburgh: Section A 144, 1067-1084 (2014)

Tao, Y., Winkler, M.:
 Dominance of chemotaxis in a chemotaxis-haptotaxis model.
 Nonlinearity 27 (6), 1225-1239 (2014)

Winkler, M.:
 Stabilization in a two-dimensional chemotaxis-Navier-Stokes system.
 Archive for Rational Mechanics and Analysis 211 (2), 455-487 (2014) <Preprint>

Winkler, M:
 How far can chemotactic cross-diffusion enforce exceeding carrying capacities?
 Journal of Nonlinear Science 24, 809-855 (2014) <Preprint>

Winkler, M.:
 Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening.
 Journal of Differential Equations 257 (4), 1056-1077 (2014) <Preprint>

2013

Brunovsky, P., Cerny, A., Winkler, M.:
  A singular differential equation stemming from an optimal control problem in financial economics.
  Applied Mathematics and Optimization 68 (2), 255-274 (2013) <Preprint>

Hillen, T., Painter, K.J., Winkler, M.:
 Convergence of a cancer invasion model to a logistic chemotaxis model.
 Mathematical Models and Methods in the Applied Sciences 23 (1), 165-198

Hillen, T., Painter, K.J., Winkler, M.:
 Anisotropic Diffusion in Oriented Environments can lead to Singularity Formation.
 European Journal of Applied Mathematics 24 (3), 371-413 (2013)

Tao, Y., Winkler, M.:
 Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion.

 Annales de l'Institut Henri Poincaré -- Analyse Non Lineaire 30 (1), 157-178 (2013) <Preprint>

Tello, J.I., Winkler, M.:
 Reduction of critical mass in a chemotaxis system by external application of chemoattractant.
 Annali della Scuola normale superiore di Pisa, Classe di Scienze 12 (5), 833-862 (2013) <Preprint>

Winkler, M.:
 Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system.
 Journal de Mathématiques Pures et Appliquees 100 (5), 748-767 (2013) <Preprint>

Winkler, M.:
  Spatially monotone homoclinic orbits in nonlinear parabolic equations of super-fast diffusion type.
 Math. Ann. 355, no. 2, 519–549 (2013) <Preprint>

2012

Fila, M., Vázquez, J.L., Winkler, M., Yanagida, E.:
 Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation.
 Archive for Rational Mechanics and Analysis 204, 599-625

Souplet, Ph., Winkler, M.:
  Classification of large-time behaviors in a reaction-diffusion system modeling diallelic selection.
  Mathematical Biosciences 239, 191-206 (2012)

Stinner, C., Tello, J.I., Winkler, M.:
 Mathematical analysis of a model of chemotaxis arising from morphogenesis.
 Mathematical Methods in the Applied Sciences 35 (4), 373-496

Tao, Y., Winkler, M.:
 Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant.
 Journal of Differential Equations 252 (3), 2520-2543 <Preprint>

Tao, Y., Winkler, M.:
 Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity.
 Journal of Differential Equations 252 (1), 692-715 <Preprint>

Tao, Y., Winkler, M.:
 Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion.
 Discrete and Continuous Dynamical Systems - A 32 (5), 1901-1914 <Preprint>

Tello, J.I., Winkler, M.:
 Stabilization in a two-species chemotaxis system with logistic source.
 Nonlinearity 25 (5), 1413-1425

Wang, Z.A., Winkler, M., Wrzosek, D.:
 Global regularity vs. infinite-time singularity formation in a chemotaxis model with volume filling effect and degenerate diffusion.
 SIAM Journal of Mathematical Analysis 44 (5), 3502-3525

Winkler, M.:
 Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops.
 Communications in Partial Differential Equations 37 (2), 319-351 <Preprint>

Winkler, M.:
 Infinite-time gradient blow-up in a degenerate parabolic equation.
 International Journal of Dynamical Systems and Differential Equations 4 (Special Issue), 126-153 <Preprint>

2011

Fila, M., King, J.R., Winkler, M., Yanagida, E.:
 Very slow grow-up of solutions of a semilinear parabolic equation.
 Proc. Roy. Soc. Edinburgh Sect. A 54 (2), 381-400 <Preprint>

Fila, M., Vázquez, J.L., Winkler, M.:
 A Continuum of Extinction Rates for the Fast Diffusion Equation.
 Communications in Pure and Applied Analysis 10 (4), 1129-1147

Souplet, Ph., Winkler, M.:
  The influence of space dimension on the large-time behavior in a reaction-diffusion system modeling diallelic selection.
 Journal of Math.~Biology 62 (3), 391-421 <Preprint>

Stinner, C., Winkler, M.:
 Global weak solutions in a chemotaxis system with large singular sensitivity.
  Nonlinear Analysis: Real World Applications 12, 3727-3740

Tao, Y., Winkler, M.:
 A chemotaxis-haptotaxis model: the roles of porous medium diffusion and logistic source.
 SIAM Journal of Mathematical Analysis 43 (2), 685-704 <Preprint>

Vázquez, J.L., Winkler, M.:
 The evolution of singularities in fast diffusion equations. Infinite-time blow-down.
 SIAM Journal of Mathematical Analysis 43 (4), 1499-1535

Vázquez, J.L., Winkler, M.:
 Highly time-oscillating solutions for very fast diffusion equations.
 Journal of Evolution Equations 11 (3), 725-742 <Preprint>

Wang, Z.A., Winkler, M., Wrzosek, D.:
 Singularity formation in chemotaxis systems with volume-filling effect.
 Nonlinearity 24 (12), 3279-3297

Winkler, M.:
  Global solutions in higher dimensions to a fourth order parabolic equation modeling epitaxial thin film growth.
 Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 62 (4), 575-608 <Preprint>

Winkler, M.:
 Global solutions in a fully parabolic chemotaxis system with singular sensitivity.
 Mathematical Methods in the Applied Sciences 34 (2), 176--190 <Preprint>

Winkler, M.:
 Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction.
 Journal of Mathematical Analysis and Applications 384, 261-272 <Preprint>

2010

Djie, K., Winkler, M.:
 Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect.
 Nonlinear Analysis: Theory, Methods and Applications 72 (2), 1044-1064 <Preprint>

Winkler, M.:
 Refined asymptotics for entire solutions of a biharmonic equation with a supercritical nonlinearity.
 Mathematische Annalen 348 (3), 633-666 <Preprint>

Winkler, M.:
 Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source.
 Communications in Partial Differential Equations 35, 1516-1537 <Preprint>

Winkler, M.:
 Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model.
 Journal of Differential Equations 248, 2889-2905 <Preprint>

Winkler, M.:
 Does a 'volume-filling effect' always prevent chemotactic collapse?
 Mathematical Methods in the Applied Sciences 33, 12-24 <Preprint>

Winkler, M.:
 Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity.
 Mathematische Nachrichten 283 (11), 1664-1673

2009

Fila, M., Winkler, M.:
 Stabilization of solutions of a semilinear parabolic equation modelling quorum sensing in a biofilm.
 Asymptotic Analysis 62, 89-106

Winkler, M.:
 Infinite-time quenching in fast diffusion equations.
 Nonlinear Differential Equations and Applications 16 (1), 41-61 <Preprint>

2008

Cieslak, T., Winkler, M.:
 Finite-time blow-up in a quasilinear system of chemotaxis.
 Nonlinearity 21, 1057-1076

Fila, M., King, J.R., Winkler, M., Yanagida, E.:
 Linear Behaviour of Solutions of a Superlinear Heat Equation.
 Journal of Math.~Analysis and its Applications 340, 401-409

Fila, M., Winkler, M.:
 Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed.
 Journal of the European Mathematical Society 10 (1), 105-132 <Preprint>

Fila, M., Winkler, M.:
 Rate of convergence to a singular steady state of a supercritical parabolic equation.
 Journal of Evolution Equations 8, 673-692

Fila, M., Winkler, M., Yanagida, E.:
 Slow Convergence to Zero for a Parabolic Equation with Supercritical Nonlinearity.
 Mathematische Annalen 340, 477-496

Fila, M., Winkler, M., Yanagida, E.:
 Convergence to selfsimilar solutions for a semilinear parabolic equation.
 Discrete Contin. Dyn. Syst. 21, 703-716

Fila, M., Winkler, M., Yanagida, E.:
 Convergence of solutions of a semilinear parabolic equation to self-similar solutions of the linear heat equation.
 Adv. Differ. Equ. 13, 1131-1149 

Stinner, C., Winkler, M.:
 Finite time vs. infinite time gradient blow-up in a degenerate diffusion equation.
 Indiana Univ. Math. Journal 57 (5), 2321-2354

Winkler, M.:
 Conservation of boundary decay and nonconvergent bounded gradients in degenerate diffusion problems.
 Advances in Differential Equations 13 (1-2), 27-54 <Preprint>
 
Winkler, M.:
 Oscillating solutions and large ω-limit sets in a degenerate parabolic equation.
 Journal of Dynamics and Differential Equations 20 (1), 87-113 <Preprint>

Winkler, M.:
 Boundedness and exponential stabilization in a signal transduction model with diffusion.
 Math. Methods in the Applied Sciences 31, 1905-1921

Winkler, M.:
 Chemotaxis with logistic source: Very weak global solutions and boundedness properties.
 Journal of Math. Analysis and Applications 348, 708-729 <Preprint>

Winkler, M.:
 The evolution of dead cores in strongly degenerate diffusion problems.
 Advances in Differential Equations 13 (11-12), 1001-1030

2007

Fila, M., King, J.R., Winkler, M., Yanagida, E.:
 Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent.
 Advances in Differential Equations 12 (1), 1-26

Fila, M., Taskinen, J., Winkler, M.:
 Convergence to a singular steady state of a parabolic equation with gradient blow-up.
 Applied Mathematics Letters 20, 578-582

Stinner, C., Winkler, M.:
 Boundedness vs. blow-up in a degenerate diffusion equation with gradient nonlinearity.
 Indiana Univ. Math. Journal 56 (5), 2233-2262

Tello, J.I., Winkler, M.:
 A chemotaxis system with logistic source.
 Communications in Partial Differential Equations 32 (6), 849-877

Winkler, M.:
 Nontrivial ordered ω-limit sets in a linear degenerate parabolic equation.
 Discrete and Continuous Dynamical Systems 17 (4), 739-750 <Preprint>

Winkler, M.:
 Nonuniqueness in the quenching problem.
 Mathematische Annalen 339, 559-597 <Preprint>

2006

Fila, M., King, J.R., Winkler, M., Yanagida, E.:
 Optimal lower bound of the grow-up rate for a supercritical parabolic equation.
 Journal of Differential Equations 228, 339-356

2005

Fila, M., Winkler, M., Yanagida, E.:
 Convergence rate for a parabolic equation with supercritical nonlinearity.
 Journal of Dynamics and Differential Equations 17 (2), 249-269

Horstmann, D., Winkler, M.:
  Boundedness vs.~blow-up in a chemotaxis system.
 Journal of Differential Equations 215 (1), 52-107

Stein, O., Winkler, M.:
 Amorphous molecular beam epitaxy: global solutions and absorbing sets.
 European Journal of Applied Mathematics 16 (6), 767-798

Winkler, M.:
 Large time behavior and stability of equilibria of degenerate parabolic equations.
 Journal of Dynamics and Differential Equations 17 (2), 331-351

2004

Fila, M., Winkler, M., Yanagida, E.:
 Grow-up rate for solutions of a Supercritical Semilinear Diffusion Equation.
 Journal of Differential Equations 205, 365-389

Quittner, P., Souplet, Ph., Winkler, M.:
 Initial blow-up rates and universal bounds for nonlinear heat equations.
 Journal of Differential Equations 196, 316-339

Winkler, M.:
 Universal bounds for a forced porous medium equation.
 Nonlinear Analysis 57, 349-362

Winkler, M.:
 Blow-up in a degenerate parabolic equation.
 Indiana Univ. Math.~Journal 53 (5), 1415-1442
 
Winkler, M.:
 A doubly critical degenerate parabolic problem.
 Math. Methods in the Applied Sciences 27 (14), 1619-1627

Winkler, M.:
 A strongly degenerate diffusion equation with strong absorption.
 Math. Nachrichten 277, 83-101

Winkler, M.:
 Instantaneous shrinking of the support in degenerate parabolic equations with strong absorption.
 Advances in Differential Equations 9 (5-6), 625-643

Winkler, M.:
 Propagation vs. constancy of support in the degenerate parabolic equation ut=f(t)Δu.
 Rend. Istit. Mat. Univ. Trieste XXXVI, 1-15

2003

King, B.B., Stein, O., Winkler, M.:
 A fourth order parabolic equation modelling epitaxial thin film growth. 
 Journal of Math. Analysis and Applications 286, 459-490

Winkler, M.:
 Blow-up of solutions to a degenerate parabolic equation not in divergence form.
 Journal of Differential Equations 192 (2) 445-474

Winkler, M.:
 Boundary behavior in strongly degenerate parabolic equations.
 Acta Math. Univ. Comenianae 72 (1), 129-139

Winkler, M.:
 Quenching phenomena in strongly degenerate diffusion equations with strong absorption.
 Journal of Math. Analysis and Applications 288, 481-504

2002

Winkler, M.:
 A critical exponent in a degenerate parabolic equation.
 Math. Methods in the Applied Sciences 25 (11), 911-925 <Preprint>

2001

Winkler, M.:
 Large time behavior of solutions to degenerate parabolic equations with absorption.
 Nonlinear Differential Equations and Applications 8 (3), 343-361

Winkler, M.:
 On the Cauchy problem for a degenerate parabolic equation.
 Zeitschrift für Analysis und ihre Anwendungen 20 (3), 677-690

 

 

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