Unboundedness for solutions to a degenerate drift-diffusion equation with the \(L^{1}\)-supercritical and the energy subcritical exponent
type: Item
instance of: scholarly article
title: Unboundedness for solutions to a degenerate drift-diffusion equation with the \(L^{1}\)-supercritical and the energy subcritical exponent
zbMATH Open document ID: 1390.35026
author: Hiroshi Wakui
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-03-22T00:00:00Z
review text: The author studies the large time behavior of weak solutions to a degenerate drift-diffusion system related to Smoluchowski-Poisson and Keller-Segel models \[ u_t=\Delta(u^\alpha)-\nabla\cdot(\rho\nabla\psi), \] \[ -\Delta\psi=\rho. \] For \(\alpha\in[\frac{2n}{n+2},2-\frac2n]\), i.e. in the range of \(\alpha\) between the energy and the \(L^1\) critical cases, this asymptotics is classified by the invariant norms of initial data and initial values of energy/entropy functional.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K59
zbMATH DE Number: 6852179
zbMATH Keywords: Patlak-Keller-Segel system
zbMATH Keywords: scaling invariance
zbMATH Keywords: Hardy-Littlewood-Sobolev inequality
zbMATH Keywords: virial law
zbMATH Keywords: Smoluchowski-Poisson models
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.12.040
OpenAlex ID: W2776100834
cites work: Q4225524
cites work: The Debye system: existence and large time behavior of solutions
cites work: Blowup of solutions to generalized Keller-Segel model
cites work: Q4833251
cites work: Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
cites work: Q3431715
cites work: On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
cites work: Initiation of slime mold aggregation viewed as an instability
cites work: Threshold of global behavior of solutions to a degenerate drift-diffusion system in between two critical exponents
cites work: Fluid mechanical approximation to the degenerated drift-diffusion system from the compressible Navier-Stokes-Poisson system
cites work: Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type.
cites work: Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
cites work: Analysis.
cites work: Q5495397
cites work: An Initial Value Problem from Semiconductor Device Theory
cites work: Global existence of solutions to a parabolic system for chemotaxis in two space dimensions
cites work: Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
cites work: Global existence of solutions to a parabolic-elliptic system of drift-diffusion type in \(\mathbb{R}^2\)
cites work: The degenerate drift-diffusion system with the Sobolev critical exponent
cites work: Non-uniform bound and finite time blow up for solutions to a drift–diffusion equation in higher dimensions
cites work: Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems.
cites work: Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
cites work: Free energy and self-interacting particles
cites work: Degenerate parabolic equation with critical exponent derived from the kinetic theory: I: Generation of the weak solution
cites work: Degenerate parabolic equation with critical exponent derived from the kinetic theory. II: Blowup threshold.
cites work: On a nonlinear elliptic equation arising in a free boundary problem
DOI: 10.1016/J.JMAA.2017.12.040
description: scientific article; zbMATH DE number 6852179