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Parabolic reaction-diffusion systems with nonlocal coupled diffusivity terms
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Orientador(es)
Resumo(s)
In this work we study a system of parabolic reaction-diffusion equations which are coupled not only through the reaction terms but also by way of nonlocal diffusivity functions. For the associated initial problem, endowed with homogeneous Dirichlet or Neumann boundary conditions, we prove the existence of global solutions. We also prove the existence of local solutions but with less assumptions on the boundedness of the nonlocal terms. The uniqueness result is established next and then we find the conditions under which the existence of strong solutions is assured. We establish several bow-up results for the strong solutions to our problem and we give a criterium for the convergence of these solutions towards a homogeneous state.
Descrição
Palavras-chave
Asymptotic-behavior Time behavior Blow-Up Equations Uniqueness Existence
Contexto Educativo
Citação
Editora
Amer Inst Mathematical Sciences-Aims