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

DOI10.1142/S0218202512500418zbMath1263.35131arXiv1110.3525OpenAlexW2963948262MaRDI QIDQ4649861

Ansgar Jüngel, Sabine Hittmeir, José Antonio Carrillo

Publication date: 15 November 2012

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.3525

zbMATH Keywords

global existencedegenerate diffusiongradient estimatesentropy functionalparabolic-parabolic modelnonlinear cross-diffusionnonlinear cell diffusionparabolic-elliptic model

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Blow-up in context of PDEs (35B44) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (20)

A nonnegativity preserving scheme for the relaxed Cahn–Hilliard equation with single-well potential and degenerate mobility ⋮ Fully decoupled and energy stable BDF schemes for a class of Keller-Segel equations ⋮ Global existence and convergence rates to a chemotaxis-fluids system with mixed boundary conditions ⋮ Backward parabolicity, cross-diffusion and Turing instability ⋮ Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality ⋮ Finite element analysis of a Keller-Segel model with additional cross-diffusion and logistic source. II: Time convergence and numerical simulation ⋮ High-order finite difference approximation of the Keller-Segel model with additional self- and cross-diffusion terms and a logistic source ⋮ A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis ⋮ How far can chemotactic cross-diffusion enforce exceeding carrying capacities? ⋮ Vanishing cross-diffusion limit in a Keller-Segel system with additional cross-diffusion ⋮ Convergence to equilibria of global solutions to a degenerate quasilinear Keller-Segel system ⋮ Finite element approximation of a Keller-Segel model with additional self- and cross-diffusion terms and a logistic source ⋮ A note on Aubin-Lions-Dubinskiĭ lemmas ⋮ Finite element analysis of a Keller-Segel model with additional cross-diffusion and logistic source. I: Space convergence ⋮ Keller-Segel chemotaxis models: a review ⋮ Analysis of a chemotaxis system modeling ant foraging ⋮ Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics ⋮ A Convergent Structure-Preserving Finite-Volume Scheme for the Shigesada--Kawasaki--Teramoto Population System ⋮ On a class of Keller-Segel chemotaxis systems with cross-diffusion ⋮ Self-organized populations interacting under pursuit-evasion dynamics

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