How Far Can Chemotactic Cross-diffusion Enforce Exceeding Carrying Capacities?

Finite-time blow-up in the higher-dimensional parabolic–parabolic Keller–Segel system

(2013) Michael Winkler   JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

Finite-time blowup and global-in-time unbounded solutions to a parabolic–parabolic quasilinear Keller–Segel system in higher dimensions

(2012) Tomasz Cieślak et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL

(2012) JOSÉ ANTONIO CARRILLO et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Spatial pattern formation in a chemotaxis–diffusion–growth model

(2012) Kousuke Kuto et al.   PHYSICA D-NONLINEAR PHENOMENA

Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction

(2011) Michael Winkler   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source

(2010) Michael Winkler   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model

(2010) Michael Winkler   JOURNAL OF DIFFERENTIAL EQUATIONS

Global existence of solutions to a parabolic–parabolic system for chemotaxis with weak degradation

(2010) E. Nakaguchi et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Spatio-temporal chaos in a chemotaxis model

(2010) Kevin J. Painter et al.   PHYSICA D-NONLINEAR PHENOMENA

Volume Filling Effect in Modelling Chemotaxis

(2010) D. Wrzosek   Mathematical Modelling of Natural Phenomena

Finite time blow-up for a one-dimensional quasilinear parabolic–parabolic chemotaxis system

(2009) Tomasz Cieślak et al.   ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

Traveling waves for the Keller–Segel system with Fisher birth terms

(2009) Gregoire Nadin et al.   INTERFACES AND FREE BOUNDARIES

Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System

(2009) Jan Haškovec et al.   JOURNAL OF STATISTICAL PHYSICS

MATHEMATICAL MODELLING OF CANCER INVASION OF TISSUE: THE ROLE AND EFFECT OF NONLOCAL INTERACTIONS

(2009) ZUZANNA SZYMAŃSKA et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect

(2009) Michael Winkler et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Global Existence for a Kinetic Model of Chemotaxis via Dispersion and Strichartz Estimates

(2008) Nikolaos Bournaveas et al.   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

A user’s guide to PDE models for chemotaxis

(2008) T. Hillen et al.   JOURNAL OF MATHEMATICAL BIOLOGY

Finite-time blow-up in a quasilinear system of chemotaxis

(2008) Tomasz Cieślak et al.   NONLINEARITY