Blow-up phenomena in chemotaxis systems with a source term

New critical exponents in a fully parabolic quasilinear Keller–Segel system and applications to volume filling models

(2015) Tomasz Cieślak et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source

(2015) Johannes Lankeit   JOURNAL OF DIFFERENTIAL EQUATIONS

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

(2015) N. Bellomo et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening

(2014) Michael Winkler   JOURNAL OF DIFFERENTIAL EQUATIONS

Finite-Time Blowup in a Supercritical Quasilinear Parabolic-Parabolic Keller-Segel System in Dimension 2

(2013) Tomasz Cieślak et al.   ACTA APPLICANDAE MATHEMATICAE

Nondegeneracy of blow-up points for the parabolic Keller–Segel system

(2013) Noriko Mizoguchi et al.   ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

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

Boundedness in a quasilinear parabolic–parabolic Keller–Segel system with subcritical sensitivity

(2011) Youshan Tao et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

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

(2011) Michael Winkler   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Lower bounds for blow-up in a model of chemotaxis

(2011) L.E. Payne et al.   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

Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, II

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

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

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

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

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

(2008) Tomasz Cieślak et al.   NONLINEARITY