Acta Applicandae Mathematicae

, Volume 102, Issue 1, pp 37–56 | Cite as

Solution and Asymptotic Behaviour for a Nonlocal Coupled System of Reaction-Diffusion

  • Carlos Alberto Raposo
  • Mauricio Sepúlveda
  • Octavio Vera Villagrán
  • Ducival Carvallo Pereira
  • Mauro Lima Santos
Article

Abstract

This paper concerns with the existence, uniqueness and asymptotic behaviour of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and exponential decay of solutions by the classic energy method. We improve the results obtained by Chipot-Lovato and Menezes for coupled systems. A numerical scheme is presented.

Keywords

Coupled system of reaction-diffusion The Faedo-Galerkin method Asymptotic behaviour Numerical methods 

Mathematics Subject Classification (2000)

35K57 35B35 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Carlos Alberto Raposo
    • 1
  • Mauricio Sepúlveda
    • 2
  • Octavio Vera Villagrán
    • 3
  • Ducival Carvallo Pereira
    • 4
  • Mauro Lima Santos
    • 4
  1. 1.UFSJSão João del-ReiBrazil
  2. 2.CI²MA and Departamento de Ingeniería MatemáticaUniversidad de ConcepciónConcepciónChile
  3. 3.Departamento de MatemáticaUniversidad del Bío-BíoConcepciónChile
  4. 4.UFPAParáBrazil

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