Soluções clássicas para um problema de combustão em meios porosos com n camadas

• Ano de defesa: 2019
• Autor(a) principal: Batista, Marcos Roberto
• Orientador(a): Mota, Jesus Carlos da
• Banca de defesa: Mota, Jesus Carlos da, Silva, Edcarlos Domingos da, Carvalho, Marcos Leandro Mendes, Ercole, Grey, Santos, Marcelo Martins dos
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em Matemática (IME)
• Departamento: Instituto de Matemática e Estatística - IME (RG)
• País: Brasil
• Palavras-chave em Português: Combustão em meios porosos; Reação-difusão; Método iterativo monótono; Soluções fundamentais; Solução maximal
• Palavras-chave em Inglês: Combustion in porous media; Reaction-diffusion; Monotone iterative method; Fundamental solutions; Maximal solution
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/10001

In this work, we study the classical solutions for a parabolic system of reaction-diffusion-convection equations, coupled to a system of ordinary differential equations, with boundary and initial conditions in a bounded domain. The coupled system models the propagation of a combustion front through a porous medium with n layers, where the dependent variables are the temperatures and the fuel concentrations in each layer. Problems for parabolic equations systems coupled with Ordinary Differential Equations (ODEs) system, where the coupling occurs in both the reaction functions and the associated differential operator coefficients, are little known in the literature. In classical theory in general, the coupling appears only in the reaction functions. Initially, using the Monotone Iterative Method, we prove the existence and uniqueness of a global solution in time for the particular case where the fuel concentrations in each layer are known functions. Next, we show the existence of the local solution in time for the complete problem when the concentrations are unknown functions. The proof is obtained by defining an operator in the Continuous Hölder function set and showing that it has a fixed point that is a local solution to the problem. This solution can be extended to a global solution in time for the problem, provided that the spatial derivatives of the temperature in each layer are bounded functions.