The Parabolic-Parabolic Keller-Segel System with Critical Diffusion as a Gradient Flow in ℝd,d ≥ 3

DOI10.1080/03605302.2012.757705zbMath1282.35202arXiv1203.3573OpenAlexW2062302699MaRDI QIDQ2841164

Philippe Laurençot, Adrien Blanchet

Publication date: 24 July 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3573

zbMATH Keywords

degenerate diffusioncritical thresholdmodified Hardy-Littlewood-Sobolev inequalityporous-medium type diffusionminimizing scheme

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Critical exponents in context of PDEs (35B33) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Degenerate parabolic equations (35K65) Initial value problems for second-order parabolic systems (35K45) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44)

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