Ondas viajantes para um problema de EDP Parabólico

• Autor(a) principal: Garzon, Brayan Mauricio Rodriguez
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000003csd
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6138
• topic: Combustão; In-situ; Meio poroso; Método melnikov; Perturbação singular; Combustion; In-situ; Melnikov method; Porous medium; Traveling waves; Singular perturbation; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work we study and show the existence of traveling waves solutions for a system of parabolic partial differential equations (PPDE’s) which model in-situ combustion process in porous medium. The in-situ combustion process is a thermal method to recovery oil from petrolific reservoirs. The system deduction is making considering two layers of porous rock and aplying the physical laws of balance energy, fuel mass, oxygen mass, total gas mass, and the Darcy’s law which link the pressure and volumetric flow rate. The traveling waves are obtained making an useful variavel change such that convert the PPDE’s system in an ordinary differential equations system (ODE’s) where the existence of heteroclinic orbits is equivalent to the existence of a traveling waves for the system of PPDE’s which connect the burned state to the unburned state. In the proof of the existence and uniquess of such orbits are used basic tools in Qualitative Ordinary Differential Equations Theory, Dynamical Systems, Perturbation Theory and TravelingWaves Theory with special mention to Singular Perturbation Theory and Melnikov Method inside of the perturbation theory.