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Volume 8, Number 3, 2018, Pages 836-858                                                                DOI:10.11948/2018.836
Asymptotic behavior in chemical reaction-diffusion systems with boundary equilibria
Michel Pierre,Takashi Suzuki,Haruki Umakoshi
Keywords:reaction-diffusion systems, asymptotic behavior of solution, convergence to equilibrium
Abstract:
      We consider the asymptotic behavior for large time of solutions to reaction-diffusion systems modeling reversible chemical reactions. We focus on the case where multiple equilibria exist. In this case, due to the existence of so-called "boundary equilibria", the analysis of the asymptotic behavior is not obvious. The solution is understood in a weak sense as a limit of adequate approximate solutions. We prove that this solution converges in L^1 toward an equilibrium as time goes to infinity and that the convergence is exponential if the limit is strictly positive.
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