Large-time approximation of a solution to a reaction-diffusion system with a balance law by its spatial average

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Abstract

A reaction-diffusion system which has a balance law is studied. Homogeneous Neumann boundary conditions are imposed. When a nonnegative global solution uniformly converges to a steady state with a polynomial rate as time goes to infinity, it is proved that the spatial average of the solution to the system describes a large-time approximation of the solution itself with an exponential rate being sharper than those obtained before. The proof is based on properties of a solution for the corresponding system of ordinary differential equations and an L estimate of an analytic semigroup.

Original languageEnglish
Pages (from-to)85-96
Number of pages12
JournalAnalysis (Germany)
Volume22
Issue number1
DOIs
Publication statusPublished - 01-01-2002

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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