Uniqueness and regularity of weak solutions for the 1-D degenerate Keller-Segel systems

DOI10.1016/j.na.2010.06.003zbMath1201.35008OpenAlexW2015291658MaRDI QIDQ988874

Yoshie Sugiyama

Publication date: 19 August 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.06.003

zbMATH Keywords

Aronson-Bénilan estimate

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Reaction-diffusion equations (35K57) Weak solutions to PDEs (35D30) Initial value problems for second-order parabolic systems (35K45) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (7)

A note on \(L^\infty\)-bound and uniqueness to a degenerate Keller-Segel model ⋮ Finite speed of propagation in 1-D degenerate Keller-Segel system ⋮ Uniqueness theorem on weak solutions to the Keller-Segel system of degenerate and singular types ⋮ Propagation of chaos for the Keller-Segel equation over bounded domains ⋮ Refined hyper-contractivity and uniqueness for the Keller-Segel equations ⋮ Uniqueness and continuity of solution for the initial data in the scaling invariant class of the degenerate Keller-Segel system ⋮ Uniqueness of weak solutions to a high dimensional Keller-Segel equation with degenerate diffusion and nonlocal aggregation

Cites Work

• Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems.
• Time global existence and asymptotic behavior of solutions to generate quasi-linear parabolic systems of chemotaxis.
• Aronson-Bénilan type estimate and the optimal Hölder continuity of weak solutions for the 1-D degenerate Keller-Segel systems
• Initiation of slime mold aggregation viewed as an instability
• Nonlinear aspects of chemotaxis
• Nonlinear evolution equations in an arbitrary Banach space
• Application of the best constant of the Sobolev inequality to degenerate Keller-Segel models
• Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
• Finite speed of propagation in 1-D degenerate Keller-Segel system
• Asymptotic profile with the optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases
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