Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case
type: Item
instance of: scholarly article
title: Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case
zbMATH Open document ID: 1479.35540
author: Takayoshi Ogawa
author: Takeshi Suguro
published in: Journal of Differential Equations
publication date: 2021-11-25T00:00:00Z
review text: A drift-diffusion system of mean field type involving singular diffusion \(\Delta u^\alpha\), \(1-1/n<\alpha<1\), and a nonlocal transport term is considered in \(\mathbb R^n\), \(n\ge 3\). The main result is that the asymptotically long time behavior of global-in-time solutions is described by generalized Barenblatt self-similar solutions. Rényi type entropy functional is used together with suitable a~priori estimates.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35C06
zbMATH DE Number: 7433260
zbMATH Keywords: drift-diffusion equation
zbMATH Keywords: fast diffusion
zbMATH Keywords: nonlocal transport term
zbMATH Keywords: asymptotic behavior of solutions
zbMATH Keywords: Rényi entropy
zbMATH Keywords: Barenblatt self-similar solutions
MaRDI profile type: Publication
full work available at URL: j.jde.2021.10.032
OpenAlex ID: W3214614929
cites work: Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent \(m > 0\)
cites work: Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems
cites work: Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
cites work: Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2
cites work: Ground states in the diffusion-dominated regime
cites work: Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
cites work: Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations
cites work: Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
cites work: Rényi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
cites work: Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
cites work: Interpolation inequalities, nonlinear flows, boundary terms, optimality and linearization
cites work: Improved interpolation inequalities, relative entropy and fast diffusion equations
cites work: Nonlinear diffusions: extremal properties of Barenblatt profiles, best matching and delays
cites work: Logarithmic Sobolev Inequalities
cites work: Entropy Methods for Diffusive Partial Differential Equations
cites work: Decay Estimates and Large Time Behavior of Solutions to the Drift-Diffusion System
cites work: Finite-time blow-up for solutions to a degenerate drift-diffusion equation for a fast-diffusion case
cites work: Asymptotic profile with the optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases
cites work: Decay Properties and Asymptotic Profiles of Bounded Solutions to a Parabolic System of Chemotaxis in Rn
cites work: A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. I
cites work: Asymptotic stability of a decaying solution to the Keller-Segel system of degenerate type.
cites work: Non-uniform bound and finite time blow up for solutions to a drift–diffusion equation in higher dimensions
cites work: Stability and instability of solutions to the drift-diffusion system
cites work: THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
cites work: A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. II
cites work: The Concavity of Rényi Entropy Power
cites work: A Mathematical Theory of Communication
cites work: Some inequalities satisfied by the quantities of information of Fisher and Shannon
cites work: Extinction, decay and blow-up for Keller-Segel systems of fast diffusion type
cites work: Shannon's inequality for the Rényi entropy and an application to the uncertainty principle
cites work: Best constant in Sobolev inequality
cites work: Q4893906
cites work: Q5489390
cites work: Q3409342
cites work: Logarithmic Sobolev Inequalities for the Heat-Diffusion Semigroup
cites work: Q3283690
DOI: 10.1016/J.JDE.2021.10.032
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description: scientific article; zbMATH DE number 7433260