Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations
type: Item
instance of: scholarly article
title: Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations
zbMATH Open document ID: 1096.35018
author: Laurent Desvillettes
author: Klemens Fellner
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-05-16T00:00:00Z
review text: The authors deal with reaction-diffusion systems including drift and modelling the transport of electrically charged species. In all previous studies a lower bound of the entropy dissipation in terms of the entropy were known, but in a nonconstructive way, that is, via a contradiction argument with no control on the constants. The goal of this paper is to provide quantitative exponential convergence to equilibrium with explicit rates and constants for reversible reaction processes of species \(A_i\), \(i= 1,2,\dots,q\), of the type \[ \alpha_1A_1+ \alpha_2A_2+\cdots+d_q A_q \rightleftarrows\beta_1A_1+\beta_2A_2+\cdots+\beta_qA_q,\;\alpha_i, \beta_i\in\mathbb{Z}_+ \] in a bounded box \(\Omega\subset \mathbb{R}^N\).
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 78A35
zbMATH DE Number: 5023164
zbMATH Keywords: entropy dissipation
zbMATH Keywords: explicit rates
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.07.003
OpenAlex ID: W1999802587
cites work: Global existence for semilinear parabolic systems.
cites work: On the Global Existence of Solutions of a Reaction-Diffusion Equation with Exponential Nonlinearity
cites work: A reaction-diffusion system with fast reversible reaction.
cites work: Long-time behavior for a nonlinear fourth-order parabolic equation
cites work: Equilibration Rate for the Linear Inhomogeneous Relaxation-Time Boltzmann Equation for Charged Particles
cites work: Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations
cites work: Q5737389
cites work: Fine Asymptotics for Fast Diffusion Equations
cites work: Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
cites work: Mathematical methods for hydrodynamic limits
cites work: Duality and entropy methods for reversible reaction-diffusion equations with degenerate diffusion
cites work: On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications
cites work: On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation
cites work: On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation
cites work: Q3995249
cites work: Convergence to global equilibrium for spatially inhomogeneous kinetic models of non-micro-reversible processes
cites work: Coupled system of reaction-diffusion equations and applications in carrier facilitated diffusion
cites work: Q4189096
cites work: Global existence and boundedness for a class of inhomogeneous semilinear parabolic systems
cites work: Stability and Lyapunov Functions for Reaction-Diffusion Systems
cites work: Free energy and dissipation rate for reaction diffusion processes of electrically charged species
cites work: Energetic Estimates and Asymptotics for Electro‐Reaction‐Diffusion Systems
cites work: On a result of K. Masuda concerning reaction-diffusion equations
cites work: Global Existence and Boundedness in Reaction-Diffusion Systems
cites work: Asymptotic behavior of global solutions for some reaction-diffusion systems
cites work: Q3705840
cites work: Global solutions of reaction-diffusion systems with a balance law and nonlinearities of exponential growth
cites work: Q3356763
cites work: Q5529067
cites work: Q3975236
cites work: On the global existence and asymptotic behavior of solutions of reaction- diffusion equations
cites work: Global Existence for Semilinear Parabolic Systems
cites work: Global solutions of reaction-diffusion systems
cites work: Q4746129
cites work: Reaction-diffusion models from the Fokker-Planck formulation ofchemical processes
cites work: A BGK MODEL FOR CHEMICAL PROCESSES: THE REACTION-DIFFUSION APPROXIMATION
cites work: Propagation of chaos for a system of annihilating brownian spheres
cites work: Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation
cites work: On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds.
cites work: Cercignani's conjecture is sometimes true and always almost true
cites work: Construction of the Leray-Schauder degree for elliptic operators in unbounded domains
cites work: Q3220397
cites work: Q5544620
DOI: 10.1016/J.JMAA.2005.07.003
description: scientific article