Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions ${n\geq 3}$
From MaRDI portal
Publication:1741662
DOI10.1007/s00220-018-3238-1zbMath1411.35140arXiv1802.03093OpenAlexW3105817979MaRDI QIDQ1741662
Michael Winkler, Philippe Souplet
Publication date: 6 May 2019
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1802.03093
Initial-boundary value problems for second-order parabolic equations (35K20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Initial-boundary value problems for mixed-type systems of PDEs (35M33) Axially symmetric solutions to PDEs (35B07)
Related Items
Exponential grow-up rates in a quasilinear Keller–Segel system, Global solutions and large time behavior for the chemotaxis-shallow water system, On refined blowup estimates for the exponential reaction-diffusion equation, Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption, Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions, Finite-time blow-up and boundedness in a 2D Keller–Segel system with rotation, Suppression of blow-up in Patlak-Keller-Segel-Navier-Stokes system via the Couette flow, Radially symmetric stationary solutions for certain chemotaxis systems in higher dimensions: a geometric approach, Critical mass for Keller–Segel systems with supercritical nonlinear sensitivity, Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems, Propagation of chaos for the Keller-Segel equation over bounded domains, Global well-posedness for aggregation equation with time-space nonlocal operator and shear flow, On the existence of global smooth solutions to the parabolic-elliptic Keller-Segel system with irregular initial data, Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher, A repertoire of repulsive Keller–Segel models with logarithmic sensitivity: Derivation, traveling waves, and quasi‐stationary dynamics, Stable singularity formation for the Keller-Segel system in three dimensions, Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system, Keller-Segel chemotaxis models: a review, Properties of blow-up solutions and their initial data for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type, The fast signal diffusion limit in nonlinear chemotaxis systems, Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions, Facing low regularity in chemotaxis systems, Dissipation enhancement of planar helical flows and applications to three-dimensional Kuramoto-Sivashinsky and Keller-Segel equations, Global radial solutions in classical Keller-Segel model of chemotaxis, The fast signal diffusion limit in Keller-Segel(-fluid) systems, A coupled 3D-1D multiscale Keller-Segel model of chemotaxis and its application to cancer invasion, Large global solutions of the parabolic-parabolic Keller-Segel system in higher dimensions, On the optimality of upper estimates near blow-up in quasilinear Keller–Segel systems, Blow-up profiles in quasilinear fully parabolic Keller–Segel systems
Cites Work
- Free energy and self-interacting particles
- A sufficient condition for type I blowup in a parabolic-elliptic system
- Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type
- A description of self-similar blow-up for dimensions n\(\geq 3\)
- Global solutions of some chemotaxis and angiogenesis system in high space dimension
- The existence of bounded solutions of a semilinear elliptic equation
- Refined uniform estimates at blow-up and applications for nonlinear heat equations
- Self-similar blow-up for a reaction-diffusion system
- Blow-up behavior for semilinear heat equations: Multi-dimensional case
- From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
- From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II
- On the stability of critical chemotactic aggregation
- Singularity patterns in a chemotaxis model
- Blowup Behavior of Radial Solutions to Jaeger-Luckhaus System in High Dimensional Domains
- Finite-time blow-up in a quasilinear system of chemotaxis
- On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
- Blow–Up Profiles in One–Dimensional. Semilinear Parabolic Problems
- Higher Dimensional Blow Up for Semilinear Parabolic Equations
- Diffusion, attraction and collapse
- Self-similar blow-up for a diffusion–attraction problem
- Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
- Existence and nonexistence of solutions for a model of gravitational interaction of particles, II
- Chemotactic collapse in a parabolic-elliptic system of mathematical biology
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
