2018 Volume 8 Issue 3
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Michel Pierre, Takashi Suzuki, Haruki Umakoshi. ASYMPTOTIC BEHAVIOR IN CHEMICAL REACTION-DIFFUSION SYSTEMS WITH BOUNDARY EQUILIBRIA[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 836-858. doi: 10.11948/2018.836
Citation: Michel Pierre, Takashi Suzuki, Haruki Umakoshi. ASYMPTOTIC BEHAVIOR IN CHEMICAL REACTION-DIFFUSION SYSTEMS WITH BOUNDARY EQUILIBRIA[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 836-858. doi: 10.11948/2018.836

ASYMPTOTIC BEHAVIOR IN CHEMICAL REACTION-DIFFUSION SYSTEMS WITH BOUNDARY EQUILIBRIA

  • 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 L1 toward an equilibrium as time goes to infinity and that the convergence is exponential if the limit is strictly positive.
    MSC: 35K61;35A01;35B40;35K57
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