Solution and asymptotic behaviour for a nonlocal coupled system of reaction-diffusion. (English) Zbl 1145.35391
Summary: 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.
MSC:
| 35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |
| 35K57 | Reaction-diffusion equations |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
Coupled system of reaction-diffusion; Faedo-Galerkin method; asymptotic behaviour; numerical methods; existence and uniqueness of weak solutions; exponential decay; numerical schemeReferences:
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