Blow-up, Concentration Phenomenon and Global Existence for the Keller–Segel Model in High Dimension
DOI10.1080/03605302.2012.655824zbMath1255.35054arXiv1003.4182OpenAlexW2023640564WikidataQ60173320 ScholiaQ60173320MaRDI QIDQ2904517
Vincent Calvez, M. A. Ebde, Lucilla Corrias
Publication date: 14 August 2012
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1003.4182
Cauchy problemglobal weak solutionenergy methodslocal weak solutionparabolic-elliptic systemsfully parabolic systems
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Continuation and prolongation of solutions to PDEs (35B60) General biology and biomathematics (92B05) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44)
Related Items (40)
Cites Work
- Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis
- Chemotactic collapse for the Keller-Segel model
- Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
- Self-similar solutions to a parabolic system modeling chemotaxis
- Critical mass phenomenon for a chemotaxis kinetic model with spherically symmetric initial data
- Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
- Initiation of slime mold aggregation viewed as an instability
- Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system
- Global solutions of some chemotaxis and angiogenesis system in high space dimension
- The parabolic-parabolic Keller-Segel model in \(\mathbb R^2\)
- Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
- A user's guide to PDE models for chemotaxis
- Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
- Nonlinear aspects of chemotaxis
- Competing symmetries, the logarithmic HLS inequality and Onofri's inequality on \(S^ n\)
- Self-similar blow-up for a reaction-diffusion system
- On the existence of radially symmetric blow-up solutions for the Keller-Segel model
- Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces
- Boundedness vs. blow-up in a chemotaxis system
- Blow-up in a chemotaxis model without symmetry assumptions
- Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2
- The Keller-Segel system of parabolic-parabolic type with initial data in weak $L^{n/2}(\mathbb{R}^n)$ and its application to self-similar solutions
- Strong solutions to the Keller-Segel system with the weakLn/2initial data and its application to the blow-up rate
- Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak–Keller–Segel Model
- 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
- On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
- Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis
- Global and Exploding Solutions for Nonlocal Quadratic Evolution Problems
- The Variational Formulation of the Fokker--Planck Equation
- Lagrangian Numerical Approximations to One‐Dimensional Convolution‐Diffusion Equations
- The 8π‐problem for radially symmetric solutions of a chemotaxis model in the plane
This page was built for publication: Blow-up, Concentration Phenomenon and Global Existence for the Keller–Segel Model in High Dimension