The Keller-Segel system of parabolic-parabolic type in Morrey space

DOI10.1016/j.jde.2018.06.017zbMath1402.35288OpenAlexW2808606375WikidataQ129687402 ScholiaQ129687402MaRDI QIDQ1671239

Fumitaka Wakabayashi

Publication date: 6 September 2018

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

Full work available at URL: https://doi.org/10.1016/j.jde.2018.06.017

zbMATH Keywords

global solutionslocal solutionsestimation of heat semigroup

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) 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) Semilinear parabolic equations (35K58) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (2)

Traveling pulse solutions of a generalized Keller-Segel system with small cell diffusion via a geometric approach ⋮ Global well-posedness and asymptotic behavior in Besov-Morrey spaces for chemotaxis-Navier-Stokes fluids

Cites Work

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• Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller-Segel equations in the whole space
• Initiation of slime mold aggregation viewed as an instability
• Global solutions of some chemotaxis and angiogenesis system in high space dimension
• The Keller-Segel system of parabolic-parabolic type with initial data in weak $L^{n/2}(\mathbb{R}^n)$ and its application to self-similar solutions
• A double scale of weighted 𝐿² spaces
• The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
• Strong solutions of the Navier-Stokes equation in Morrey spaces

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