Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller-Segel system

DOI10.1016/j.jde.2012.06.001zbMath1255.35005OpenAlexW2078475230MaRDI QIDQ444942

Yumi Yahagi, Hideo Kozono, Yoshie Sugiyama

Publication date: 24 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.06.001

zbMATH Keywords

Cauchy problem

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for second-order parabolic systems (35K45) Cell movement (chemotaxis, etc.) (92C17) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (15)

Uniqueness theorem on weak solutions to the Keller-Segel system of degenerate and singular types ⋮ Finite time blow up for a solution to system of the drift-diffusion equations in higher dimensions ⋮ On the uniqueness of mild solutions for the parabolic-elliptic Keller-Segel system in the critical \(L^p \)-space ⋮ Models of particles of the Michie-King type ⋮ Singular limit problem for the Keller-Segel system and drift-diffusion system in scaling critical spaces ⋮ Finite time blow up and concentration phenomena for a solution to drift-diffusion equations in higher dimensions ⋮ Preface ⋮ On uniqueness theorem on weak solutions to the parabolic-parabolic Keller-Segel system of degenerate and singular types ⋮ Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving \textit{BMO} ⋮ Well-posedness and unconditional uniqueness of mild solutions to the Keller-Segel system in uniformly local spaces ⋮ Stability of constant steady states of a chemotaxis model ⋮ Local well-posedness and finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions ⋮ Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space ⋮ Well-posedness of mild solutions to the drift-diffusion and the vorticity equations in amalgam spaces ⋮ Existence, uniqueness and \(L^\infty\)-bound for weak solutions of a time fractional Keller-Segel system

Cites Work

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• Global solutions of some chemotaxis and angiogenesis system in high space dimension
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• Strong solutions to the Keller-Segel system with the weakL^n/2initial data and its application to the blow-up rate
• Local solvability of the Keller–Segel system with Cauchy data in the Besov spaces
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

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