Uniqueness and long time asymptotics for the parabolic–parabolic Keller–Segel equation

DOI10.1080/03605302.2017.1280682zbMath1377.35134arXiv1406.6006OpenAlexW1520588577MaRDI QIDQ2986684

Stéphane Mischler, Kleber Carrapatoso

Publication date: 16 May 2017

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

Full work available at URL: https://arxiv.org/abs/1406.6006

zbMATH Keywords

stabilityuniquenessregularizationlong-time behaviorself-similar variablesKeller-Segel system

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) A priori estimates in context of PDEs (35B45) Continuation and prolongation of solutions to PDEs (35B60) Initial value problems for second-order parabolic systems (35K45) General biology and biomathematics (92B05) Cell movement (chemotaxis, etc.) (92C17)

Related Items (16)

Uniqueness and long time asymptotic for the Keller-Segel equation: the parabolic-elliptic case ⋮ Spectral analysis of semigroups and growth-fragmentation equations ⋮ Suppression of blow-up in parabolic–parabolic Patlak–Keller–Segel via strictly monotone shear flows ⋮ The parabolic-parabolic Keller-Segel equation ⋮ On the uniqueness of mild solutions for the parabolic-elliptic Keller-Segel system in the critical \(L^p \)-space ⋮ Suppression of blow-up in Patlak-Keller-Segel-Navier-Stokes system via the Couette flow ⋮ Global well-posedness to a chemotaxis-Stokes system ⋮ Large self-similar solutions of the parabolic-elliptic Keller-Segel model ⋮ The singular convergence of a chemotaxis-fluid system modeling coral fertilization ⋮ Global well-posedness for aggregation equation with time-space nonlocal operator and shear flow ⋮ Sharp discontinuous traveling waves in a hyperbolic Keller–Segel equation ⋮ Uniform semigroup spectral analysis of the discrete, fractional and classical Fokker-Planck equations ⋮ Time-decay estimates for Keller-Segel system ⋮ Existence and uniqueness of solutions for a hyperbolic Keller-Segel equation ⋮ Existence and regularity for a chemotaxis model involved in the modeling of multiple sclerosis ⋮ A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: the one-dimensional case

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