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On blowup dynamics in the Keller–Segel model of chemotaxis (Q2931151)

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English	On blowup dynamics in the Keller–Segel model of chemotaxis	scientific article

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scholarly article

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On blowup dynamics in the Keller–Segel model of chemotaxis (English)

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Pavel M. Lushnikov

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Israel Michael Sigal

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St. Petersburg Mathematical Journal

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publication date

24 November 2014

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full work available at URL

https://arxiv.org/abs/1304.1583

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zbMATH Keywords

collapse

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blowup profile

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MaRDI profile type

MaRDI publication profile

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Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality

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Blow-up in multidimensional aggregation equations with mildly singular interaction kernels

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Growth and accretion of mass in an astrophysical model

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Collapse of an instanton

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Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model

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Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

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Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ<sup>2</sup>

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Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model

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Diffusion, attraction and collapse

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On asymptotic stability of solitary waves for nonlinear Schrödinger equations

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Competing symmetries, the logarithmic HLS inequality and Onofri's inequality on \(S^ n\)

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Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass Keller-Segel equation

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Particle, kinetic, and hydrodynamic models of swarming

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Nonlinear aspects of chemotaxis

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Asymptotic states of a Smoluchowski equation

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Remarks on a Smoluchowski equation

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Blow-up in nonlinear heat equations

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On spectra of linearized operators for Keller-Segel models of chemotaxis

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Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis

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On soliton dynamics in nonlinear Schrödinger equations

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Relaxation of solitons in nonlinear Schrödinger equations with potential

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Mathematical concepts of quantum mechanics.

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Chemotactic collapse for the Keller-Segel model

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Singularity patterns in a chemotaxis model

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Finite-time aggregation into a single point in a reaction - diffusion system

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Self-similar blow-up for a reaction-diffusion system

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A user's guide to PDE models for chemotaxis

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The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results.

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On the existence of radially symmetric blow-up solutions for the Keller-Segel model

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From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I

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From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II

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Blow-up in a chemotaxis model without symmetry assumptions

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Boundedness vs. blow-up in a chemotaxis system

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On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis

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Initiation of slime mold aggregation viewed as an instability

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Renormalization and blow up for charge one equivariant critical wave maps

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Critical chemotactic collapse

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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

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Blow-up behavior outside the origin for a semilinear wave equation in the radial case

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Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

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Global existence and blowup of solutions to a chemotaxis system.

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Behavior of radially symmetric solutions of a system related to chemotaxis

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Chemotactic collapse in a parabolic system of mathematical biology

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On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes

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Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks

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On collapse of wave maps

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Random walk with persistence and external bias

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On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model

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Multichannel nonlinear scattering for nonintegrable equations

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Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data

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SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

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The Derivation of Chemotaxis Equations as Limit Dynamics of Moderately Interacting Stochastic Many-Particle Systems

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Equivariant wave maps in two space dimensions

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The nonlinear Schrödinger equation. Self-focusing and wave collapse

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Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions

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STABLE DIRECTIONS FOR EXCITED STATES OF NONLINEAR SCHRÖDINGER EQUATIONS

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Stability of Some Mechanisms of Chemotactic Aggregation

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Point Dynamics in a Singular Limit of the Keller--Segel Model 1: Motion of the Concentration Regions

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On steady distributions of self-attracting clusters under friction and fluctuations

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Identifiers

zbMATH Open document ID

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10.1090/S1061-0022-2014-01306-4

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2931151

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