\(\varepsilon \)-regularity theorem and its application to the blow-up solutions of Keller-Segel systems in higher dimensions

DOI10.1016/j.jmaa.2009.11.019zbMath1186.35021OpenAlexW2050234675MaRDI QIDQ847050

Yoshie Sugiyama

Publication date: 12 February 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.11.019

zbMATH Keywords

nonlinear diffusion\(\varepsilon\)-regularityparabolic-elliptic Keller-Segel systemlocal estimatesblowup set

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Initial value problems for second-order parabolic systems (35K45) Blow-up in context of PDEs (35B44)

Related Items

Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source ⋮ Extinction, decay and blow-up for Keller-Segel systems of fast diffusion type ⋮ Nondegeneracy of blow-up points for the parabolic Keller-Segel system ⋮ Blow-up behavior of solutions to a degenerate parabolic-parabolic Keller-Segel system ⋮ Properties of blow-up solutions and their initial data for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type ⋮ Partial regularity and blow-up asymptotics of weak solutions to degenerate parabolic systems of porous medium type

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