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Publikationen Winkler

2020

Li, G., Tao, Y., Winkler, M.:
 Large time behavior in a predator-prey system with indirect pursuit-evasion interaction.
 Erscheint in: Discrete and Continuous Dynamical Systems - B <Preprint>

Rodriguez, N., Winkler, M.:
 Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation.
 Erscheint in: Mathematical Models & Methods in Applied Sciences <Preprint>

Tao, Y., Winkler, M.:
 Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime.
 Erscheint in: Communications in Mathematical Sciences <Preprint>

Tao, Y., Winkler, M.:
 A critical virus production rate for efficiency of oncolytic virotherapy.
 Erscheint in: European Journal of Applied Mathematics <Preprint>

Wang, Y., Winkler, M., Xiang, Z.:
 Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption.
 Erscheint in: Science China Mathematics <Preprint>

Winkler, M.:
 Does Leray's structure theorem withstand buoyancy-driven chemotaxis-fluid interaction?
 Erscheint in: Journal of the European Mathematical Society <Preprint>

Winkler, M.:
 Does spatial homogeneity ultimately prevail in nutrient taxis systems?
A paradigm for structure support by rapid diffusion decay in an autonomous parabolic flow.

 Erscheint in: Transactions of the American Mathematical Society <Preprint>

Winkler, M.:
 A critical blow-up exponent for flux limitation in a Keller-Segel system.
 Erscheint in: Indiana University Mathematics Journal <Preprint>

Winkler, M.:
 Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions.
 Erscheint in: Advanced Nonlinear Studies <Preprint>

Winkler, M.:
 Can simultaneous density-determined enhancement of diffusion and cross-diffusion foster boundedness in Keller-Segel type systems involving signal-dependent motilities?
 Erscheint in: Nonlinearity <Preprint>

Winkler, M.:
 Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity.
 Erscheint in: Applied Mathematics Letters <Preprint>

Winkler, M.:
 Approaching critical decay in a strongly degenerate parabolic equation.
 Erscheint in: Journal of Dynamics and Differential Equations <Preprint>

Evje, S., Winkler, M.:
 Mathematical analysis of two competing cancer cell migration mechanisms driven by interstitial fluid flow.
 Journal of Nonlinear Science 30, 1809-1847 (2020) <Preprint>

Stinner, C., Winkler, M.:
 Refined regularity and stabilization properties in a degenerate haptotaxis system.
 Discrete and Continuous Dynamical Systems - A 40, 4039-4058 (2020) <Preprint>

Tao, Y., Winkler, M.:
 A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy.
 Nonlinear Analysis 198, 111870 (2020) <Preprint>

Tao, Y., Winkler, M.:
 Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy.
 Journal of Differential Equations 268, 4973-4997 (2020) <Preprint>

Winkler, M.:
 Small-mass solutions in the two-dimensional Keller-Segel system coupled to the Navier-Stokes equations.
 SIAM Journal on Mathematical Analysis 52, 2041-2080 (2020) <Preprint>

Winkler, M.:
 Can fluid interaction influence the critical mass for taxis-driven blow-up in bounded planar domains?
 Acta Applicandae Mathematicae 169, 577-591 (2020) <Preprint>

Winkler, M.:
 Single-point blow-up in the Cauchy problem for the higher-dimensional Keller-Segel system.
 Nonlinearity 33, 5007-5048 (2020) <Preprint>

Winkler, M.:
 Boundedness in a two-dimensional Keller-Segel-Navier-Stokes system involving a rapidly diffusing repulsive signal.
 Zeitschrift für Angewandte Mathematik und Physik 71, 10 (2020) <Preprint>

Winkler, M.:
 The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in $L^1$.
 Advances in Nonlinear Analysis 9, 526-566 (2020) <Preprint>

2019

Bellomo, N., Painter, K.J., Tao, Y., Winkler, M.:
 Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection.
 SIAM Journal on Applied Mathematics 79, 1990-2010 (2019)

Fila, M., Winkler, M.:
 A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation.
 Advances in Mathematics 357, 106823 (2019) <Preprint>

Krzyzanowski, P., Winkler, M., Wrzosek, D.:
 Migration-driven benefit in a two-species nutrient taxis system.
 Nonlinear Analysis 48, 94-116 (2019)

Lankeit, J., Winkler, M.:
 Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal degenerate parabolic equation
arising in game theory.

 Israel Journal of Mathematics (2019). <Preprint>
 https://doi.org/10.1007/s11856-019-1900-8

Lankeit, J., Winkler, M.:
 Facing low regularity in chemotaxis systems.
 Erscheint in: Jahresberichte der Deutschen Mathematiker-Vereinigung. <Preprint>

Souplet, Ph., Winkler, M.:
 Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $n\ge 3$.
 Communications in Mathematical Physics 367, 665-681 (2019) <Preprint>

Tao, Y., Winkler, M.:
 Boundedness and stabilization in a population model with cross-diffusion for one species.
 Proceedings of the London Mathematical Society 119, 1598-1632 (2019) <Preprint>

Tao, Y., Winkler, M.:
 Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food.
 Mathematical Models & Methods in Applied Sciences 29, 2151-2182 (2019) <Preprint>

Tao, Y., Winkler, M.:
 Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension.
 Journal of Differential Equations 267, 388-406 (2019) <Preprint>

Tao, Y., Winkler, M.:
 A chemotaxis-haptotaxis system with haptoattractant remodeling: Boundedness enforced by mild saturation of signal production.
 Communications on Pure and Applied Analysis 18, 2047-2067 (2019) <Preprint>

Wang, Y., Winkler, M., Xiang, Z.:
 The fast signal diffusion limit in Keller-Segel(-fluid) systems.
 Calculus of Variations and Partial Differential Equations 58, 196 (2019) <Preprint>

Winkler, M.:
 Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system.
 Erscheint in: Journal d'Analyse Mathématique <Preprint>

Winkler, M.:
 Does repulsion-type directional preference in chemotactic migration continue to regularize Keller-Segel systems
when coupled to the Navier-Stokes equations?

 Nonlinear Differential Equations and Applications 26, 48 (2019) <Preprint>

Winkler, M.:
 A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: Global weak solutions and asymptotic stabilization.
 Journal of Functional Analysis 276, 1339-1401 (2019) <Preprint>

Winkler, M.:
 Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis(-Stokes) systems?
 International Mathematics Research Notices (2019). <Preprint>
 https://doi.org/10.1093/imrn/rnz056

Winkler, M.:
 How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases.
 Mathematische Annalen 373, 1237-1282 (2019) <Preprint>

Winkler, M.:
 Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation.
 Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 36, 1747-1790 (2019) <Preprint>

Winkler, M.:
 Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions.
Mathematical Models & Methods in Applied Sciences 29, 373-418 (2019) <Preprint>

Winkler, M.:
 How strong singularities can be regularized by logistic degradation in the Keller-Segel system?
Annali di Matematica Pura ed Applicata 198, 1615-1637 (2019) <Preprint>
 https://doi.org/ 10.1007/s10231-019-00834-z

Winkler, M.:
 Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities.
 Journal of Differential Equations 266, 8034-8066 (2019) <Preprint>

Winkler, M.:
 Instantaneous regularization of distributions from $(C^0)^\star \times L^2$ in the one-dimensional parabolic Keller-Segel system.
Nonlinear Analysis 183, 102-116 (2019) <Preprint>

Winkler, M.:
 Boundedness in a chemotaxis-May-Nowak model for virus dynamics with mildly saturated chemotactic sensitivity.
Acta Applicandae Mathematicae 163, 1-17 (2019) <Preprint>
 https://doi.org/10.1007/s10440-018-0211-0

2018

Cao, X., Winkler, M.: 
 Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains.
 Proceedings of the Royal Society of Edinburgh: Section A: Mathematics 148, 939-955 (2018)   <Preprint>

Espejo, E., Winkler, M.:
 Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization.
 Nonlinearity 31, 1227-1259 (2018) <Preprint>

Hillen, T., Painter, K.J., Winkler, M.:
 Global solvability and explicit bounds for a non-local adhesion model.
 European Journal of Applied Mathematics 29, 645-684 (2018)

Wang, Y., Winkler, M., Xiang, Z.:
 The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system.
 Mathematische Zeitschrift 289, 71-108 (2018) <Preprint>

Wang, Y., Winkler, M., Xiang, Z.: 
 Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity.
 Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 18, 421-466 (2018)   <Preprint>

Winkler, M.:
 Singular structure formation in a degenerate haptotaxis model involving myopic diffusion.
 Journal de Mathématiques Pures et Appliquées 112, 118-169 (2018) <Preprint>

Winkler, M.:
Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity?
 Journal of Mathematical Fluid Mechanics 20, 1889-1909 (2018) <Preprint>

Winkler, M.:
 A critical blow-up exponent in a chemotaxis system with nonlinear signal production.
 Nonlinearity 31, 2031-2056 (2018) <Preprint>

Winkler, M.:
 Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation.
Zeitschrift für Angewandte Mathematik und Physik 69, Art. 69, 40 pp. (2018) <Preprint>

Winkler, M.: 
 One-dimensional super-fast diffusion: Persistence vs. extinction revisited. Extinction at spatial infinity.
 Journal of Dynamics and Differential Equations 30, 331-358 (2018) <Preprint>

Winkler, M.:
 Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption.
 Journal of Differential Equations 264, 2310-2350 (2018) <Preprint>

Winkler, M.:
 Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement.
 Journal of Differential Equations 264, 6109-6151 (2018) <Preprint>

Winkler, M.:
 Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components.
 Journal of Evolution Equations 18, 1267-1289 (2018) <Preprint>

Winkler, M., Yokota, T.:
 Stabilization in the logarithmic Keller-Segel system.
 Nonlinear Analysis 170, 123-141 (2018) <Preprint>

2017

Bellomo, N., Winkler, M.: 
 A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up.
 Communications in Partial Differential Equations 42, 436-473 (2017)   <Preprint>

Bellomo, N., Winkler, M.: 
  Finite-time blow-up in a degenerate chemotaxis system with flux limitation.
 Transactions of the American Mathematical Society B 4, 31-67 (2017)   <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>

Cieślak, T., Winkler, M.: 
 Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity.
 Nonlinear Analysis 159, 129-144 (2017) <Preprint>

Fila, M., Winkler, M.: 
 Slow growth of solutions of super-fast diffusion equations with unbounded initial data.
 Journal of the London Mathematical Society 95, 659-683 (2017) <Preprint>

Kavallaris, N., Lankeit, J., Winkler, M.: 
 On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics.
 SIAM Journal on Mathematical Analysis 49, 954-983 (2017) <Preprint>

Lankeit, J., Winkler, M.:
A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data.
 Nonlinear Differential Equations and Applications 24, Art. 49, 33 S. <Preprint>

Lou, Y., Tao, Y., Winkler, M.:
 Nonexistence of Nonconstant Steady-State Solutions in a Triangular Cross-Diffusion Model.
 Journal of Differential Equations 262, 5160-5178 (2017) <Preprint>

Surulescu, C., Winkler, M.:
 Global weak solutions to a strongly degenerate haptotaxis model.
 Communications in Mathematical Sciences 15, 1581-1616 (2017) <Preprint>

Tao, Y., Winkler, M.:
 Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production.
 Journal of the European Mathematical Society 19, 3641-3678 (2017)  <Preprint>

Tao, Y., Winkler, M.: 
 Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system.
 Mathematical Models and Methods in Applied Sciences 27, 1645-1683 (2017) <Preprint>

Winkler, M.:
  Global existence and slow grow-up in a quasilinear Keller-Segel system with exponentially decaying diffusivity.
 Nonlinearity 30, 735-764 (2017)   <Preprint>

Winkler, M.:
 Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems.
 Discrete and Continuous Dynamical Systems - B 22, 2777-2793 (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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