Gradient estimate for solutions to quasilinear non-degenerate Keller-Segel systems on \(\mathbb{R}^N\)

DOI10.3934/dcdsb.2013.18.2537zbMath1280.35020OpenAlexW2322956612MaRDI QIDQ380061

Yusuke Maeda, Tomomi Yokota, Sachiko Ishida

Publication date: 12 November 2013

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2013.18.2537

zbMATH Keywords

blow-upmodified Bernstein's methodquasilinear non-degenerate Keller-Segel systems

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Critical exponents in context of PDEs (35B33) A priori estimates in context of PDEs (35B45) Initial value problems for second-order parabolic systems (35K45) Blow-up in context of PDEs (35B44) Quasilinear parabolic equations (35K59)

Related Items (4)

Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity ⋮ How strongly does diffusion or logistic-type degradation affect existence of global weak solutions in a chemotaxis-Navier-Stokes system? ⋮ Rigorous derivation of the degenerate parabolic-elliptic Keller-Segel system from a moderately interacting stochastic particle system. I: Partial differential equation ⋮ An iterative approach to \(L^\infty\)-boundedness in quasilinear Keller-Segel systems

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