Nondegeneracy of blow-up points for the parabolic Keller-Segel system

DOI10.1016/j.anihpc.2013.07.007zbMath1302.35075OpenAlexW1974027587MaRDI QIDQ457841

Noriko Mizoguchi, Philippe Souplet

Publication date: 29 September 2014

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2013.07.007

zbMATH Keywords

Neumann boundary conditionslocal nondegeneracy

Mathematics Subject Classification ID

Initial value problems for second-order parabolic systems (35K45) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)

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Cites Work

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• Unnamed Item
• Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
• Blow-up behavior of solutions to a parabolic-elliptic system on higher dimensional domains
• Free energy and self-interacting particles
• Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type
• The two-dimensional Keller-Segel model after blow-up
• Initiation of slime mold aggregation viewed as an instability
• \(\varepsilon \)-regularity theorem and its application to the blow-up solutions of Keller-Segel systems in higher dimensions
• Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system
• The parabolic-parabolic Keller-Segel model in \(\mathbb R^2\)
• A user's guide to PDE models for chemotaxis
• Grow-up rate of a radial solution for a parabolic-elliptic system in \(\mathbb{R}^2\)
• Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
• Nonlinear aspects of chemotaxis
• Symmetrization techniques on unbounded domains: Application to a chemotaxis system on \(\mathbb{R}^N\)
• Self-similar blow-up for a reaction-diffusion system
• Measure valued solutions of the 2D Keller-Segel system
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• The \(8\pi\)-problem for radially symmetric solutions of a chemotaxis model in a disc
• Boundedness vs. blow-up in a chemotaxis system
• Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
• Singularity patterns in a chemotaxis model
• A semilinear parabolic–elliptic chemotaxis system with critical mass in any space dimension
• Semilinear Parabolic Problems Define Semiflows on C k Spaces
• Grow-Up Rate and Refined Asymptotics for a Two-Dimensional Patlak–Keller–Segel Model in a Disk
• Blowup Behavior of Radial Solutions to Jaeger-Luckhaus System in High Dimensional Domains
• Nondegeneracy of blowup for semilinear heat equations
• Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ²
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis
• Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
• Point Dynamics in a Singular Limit of the Keller--Segel Model 1: Motion of the Concentration Regions
• Asymptotic profile with the optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases
• On the growth of solutions of quasi‐linear parabolic equations
• Chemotactic collapse in a parabolic system of mathematical biology
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

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