Exponential decay towards equilibrium and global classical solutions for nonlinear reaction–diffusion systems

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• 作者：Klemens Fellner ; El-Haj Laamri
• 关键词：Reaction–diffusion systems ; Global existence ; Duality method ; Entropy method ; Convergence to equilibrium ; Exponential rates of convergence
• 刊名：Journal of Evolution Equations
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：16
• 期：3
• 页码：681-704
• 全文大小：627 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1424-3202
• 卷排序：16

文摘

We consider a system of reaction–diffusion equations describing the reversible reaction of two species \({\mathcal{U}}\), \({\mathcal{V}}\) forming a third species \({\mathcal{W}}\) and vice versa according to mass action law kinetics with arbitrary stoichiometric coefficients (equal or larger than one). Firstly, we prove existence of global classical solutions via improved duality estimates under the assumption that one of the diffusion coefficients of \({\mathcal{U}}\) or \({\mathcal{V}}\) is sufficiently close to the diffusion coefficient of \({\mathcal{W}}\). Secondly, we derive an entropy entropy-dissipation estimate, that is a functional inequality, which applied to global solutions of these reaction–diffusion systems proves exponential convergence to equilibrium with explicit rates and constants.