Singularities of solutions to chemotaxis systems

DOI10.1515/9783110599534zbMath1450.35001OpenAlexW2993490526MaRDI QIDQ2332801

Piotr Biler

Publication date: 5 November 2019

Published in: De Gruyter Series in Mathematics and Life Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/9783110599534

zbMATH Keywords

global existencefractional diffusionfinite-time blow-upparabolic-elliptic Keller-Segel systemsingular steady state

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Initial value problems for second-order parabolic systems (35K45) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Cell movement (chemotaxis, etc.) (92C17) Singularity in context of PDEs (35A21) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11) Comparison principles in context of PDEs (35B51)

Related Items (13)

Classical solutions to Cauchy problems for parabolic-elliptic systems of Keller-Segel type ⋮ Solutions to the Keller-Segel system with non-integrable behavior at spatial infinity ⋮ Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis ⋮ A simple proof of non-explosion for measure solutions of the Keller-Segel equation ⋮ Global solution to the Cauchy problem of fractional drift diffusion system with power-law nonlinearity ⋮ Evolution equations with sectorial operator on fractional power scales ⋮ Stable singularity formation for the Keller-Segel system in three dimensions ⋮ Around a singular solution of a nonlocal nonlinear heat equation ⋮ Global existence and uniform boundedness in a chemotaxis model with signal-dependent motility ⋮ A hyperbolic-elliptic-parabolic PDE model describing chemotactic \textit{E. coli} colonies ⋮ Sharp Sobolev estimates for concentration of solutions to an aggregation-diffusion equation ⋮ Large global solutions of the parabolic-parabolic Keller-Segel system in higher dimensions ⋮ Global Fujita-Kato's type solutions and long-time behavior for the multidimensional chemotaxis model

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