On blowup dynamics in the Keller–Segel model of chemotaxis

DOI10.1090/S1061-0022-2014-01306-4zbMath1326.35049arXiv1304.1583MaRDI QIDQ2931151

Daniel Egli, Pavel M. Lushnikov, Steven Dejak, Israel Michael Sigal

Publication date: 24 November 2014

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.1583

zbMATH Keywords

collapseblowup profile

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Initial-boundary value problems for second-order parabolic systems (35K51) Fokker-Planck equations (35Q84)

Related Items

Spectral analysis for singularity formation of the two dimensional Keller-Segel system ⋮ Critical chemotactic collapse ⋮ On spectra of linearized operators for Keller-Segel models of chemotaxis

Cites Work

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• On spectra of linearized operators for Keller-Segel models of chemotaxis
• Blow-up behavior outside the origin for a semilinear wave equation in the radial case
• Chemotactic collapse for the Keller-Segel model
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• On collapse of wave maps
• Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model
• Initiation of slime mold aggregation viewed as an instability
• On soliton dynamics in nonlinear Schrödinger equations
• On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model
• A user's guide to PDE models for chemotaxis
• Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
• Blow-up in nonlinear heat equations
• Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model
• On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
• Nonlinear aspects of chemotaxis
• Competing symmetries, the logarithmic HLS inequality and Onofri's inequality on \(S^ n\)
• On steady distributions of self-attracting clusters under friction and fluctuations
• Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Self-similar blow-up for a reaction-diffusion system
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• On the existence of radially symmetric blow-up solutions for the Keller-Segel model
• Asymptotic states of a Smoluchowski equation
• From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II
• On asymptotic stability of solitary waves for nonlinear Schrödinger equations
• Global existence and blowup of solutions to a chemotaxis system.
• Remarks on a Smoluchowski equation
• Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass Keller-Segel equation
• Critical chemotactic collapse
• Relaxation of solitons in nonlinear Schrödinger equations with potential
• Renormalization and blow up for charge one equivariant critical wave maps
• Boundedness vs. blow-up in a chemotaxis system
• Singularity patterns in a chemotaxis model
• Multichannel nonlinear scattering for nonintegrable equations
• Blow-up in a chemotaxis model without symmetry assumptions
• Random walk with persistence and external bias
• Particle, kinetic, and hydrodynamic models of swarming
• Stability of Some Mechanisms of Chemotactic Aggregation
• Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ²
• Blow up of the critical norm for some radial <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> super critical nonlinear Schrödinger equations
• Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
• Finite-time aggregation into a single point in a reaction - diffusion system
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis
• Diffusion, attraction and collapse
• Behavior of radially symmetric solutions of a system related to chemotaxis
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
• Equivariant wave maps in two space dimensions
• The Derivation of Chemotaxis Equations as Limit Dynamics of Moderately Interacting Stochastic Many-Particle Systems
• Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions
• STABLE DIRECTIONS FOR EXCITED STATES OF NONLINEAR SCHRÖDINGER EQUATIONS
• Collapse of an instanton
• Point Dynamics in a Singular Limit of the Keller--Segel Model 1: Motion of the Concentration Regions
• Growth and accretion of mass in an astrophysical model
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS
• Mathematical concepts of quantum mechanics.
• Chemotactic collapse in a parabolic system of mathematical biology
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
• The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results.

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