A note on \(L^\infty\)-bound and uniqueness to a degenerate Keller-Segel model

DOI10.1007/s10440-015-0022-5zbMath1335.35103OpenAlexW2465813302MaRDI QIDQ267130

Jian-Guo Liu, Jinhuan Wang

Publication date: 8 April 2016

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-015-0022-5

zbMATH Keywords

displacement convexitylog-Lipschitzstability in Wasserstein metricYudovich type theorem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell movement (chemotaxis, etc.) (92C17) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (13)

Equilibria of homogeneous functionals in the fair-competition regime ⋮ Some Compactness Criteria for Weak Solutions of Time Fractional PDEs ⋮ $L^\infty $ estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems ⋮ Supercritical degenerate parabolic-parabolic Keller-Segel system: existence criterion given by the best constant in Sobolev's inequality ⋮ On the well-posedness via the JKO approach and a study of blow-up of solutions for a multispecies Keller-Segel chemotaxis system with no mass conservation ⋮ The Geometry of Diffusing and Self-Attracting Particles in a One-Dimensional Fair-Competition Regime ⋮ A degenerate \(p\)-Laplacian Keller-Segel model ⋮ Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos ⋮ Uniform \(L^{\infty}\) boundedness for a degenerate parabolic-parabolic Keller-Segel model ⋮ Keller-Segel chemotaxis models: a review ⋮ Uniqueness of weak solutions to a high dimensional Keller-Segel equation with degenerate diffusion and nonlocal aggregation ⋮ Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime ⋮ Uniform in time \(L^{\infty }\)-estimates for nonlinear aggregation-diffusion equations

Cites Work

• Unnamed Item
• Unnamed Item
• Uniqueness and long time asymptotic for the Keller-Segel equation: the parabolic-elliptic case
• Uniqueness for Keller-Segel-type chemotaxis models
• Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent \(m > 0\)
• Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems.
• On uniqueness theorem on weak solutions to the parabolic-parabolic Keller-Segel system of degenerate and singular types
• Uniqueness of the solution to the Vlasov--Poisson system with bounded density
• Ordinary differential equations, transport theory and Sobolev spaces
• Uniqueness and regularity of weak solutions for the 1-D degenerate Keller-Segel systems
• Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
• Ultra-contractivity for Keller-Segel model with diffusion exponent \(m>1-2/d\)
• Exact criterion for global existence and blow up to a degenerate Keller-Segel system
• Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
• On classical solutions of the two-dimensional non-stationary Euler equation
• Uniqueness theorem on weak solutions to the Keller-Segel system of degenerate and singular types
• The Parabolic-Parabolic Keller-Segel System with Critical Diffusion as a Gradient Flow in ℝ^d,d ≥ 3
• The Patlak–Keller–Segel Model and Its Variations: Properties of Solutions via Maximum Principle
• Multidimensional Degenerate Keller–Segel System with Critical Diffusion Exponent $2n/(n+2)$
• Large Mass Global Solutions for a Class ofL¹-Critical Nonlocal Aggregation Equations and Parabolic-Elliptic Patlak-Keller-Segel Models

This page was built for publication: A note on \(L^\infty\)-bound and uniqueness to a degenerate Keller-Segel model