Uniqueness and continuity of solution for the initial data in the scaling invariant class of the degenerate Keller-Segel system

DOI10.1007/s00028-010-0093-8zbMath1242.35007OpenAlexW2123752015MaRDI QIDQ657035

Yoshie Sugiyama, Yumi Yahagi

Publication date: 13 January 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-010-0093-8

zbMATH Keywords

porous medium equationelliptic-parabolic system\(L ^{1}\)-contraction principle

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Quasilinear parabolic equations (35K59)

Related Items (7)

Hölder regularity and uniqueness theorem on weak solutions to the degenerate Keller-Segel system ⋮ Blow-up and delay for a parabolic-elliptic Keller-Segel system with a source term ⋮ Uniqueness theorem on weak solutions to the Keller-Segel system of degenerate and singular types ⋮ Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system ⋮ Blow-up profiles for a semilinear chemotaxis system arising in biology ⋮ The variational formulation of the fully parabolic Keller-Segel system with degenerate diffusion ⋮ The Parabolic-Parabolic Keller-Segel System with Critical Diffusion as a Gradient Flow in ℝ^d,d ≥ 3

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