Problemas de Riemann para um Sistema Simétrico de Duas Leis de Conservação

• Ano de defesa: 2010
• Autor(a) principal: LIMA, Lidiane dos Santos Monteiro
• Orientador(a): MOTA, Jesus Carlos da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Mestrado em Matemática
• Departamento: Ciências Exatas e da Terra
• País: BR
• Palavras-chave em Português: Leis de conservação; problemas de Riemann; sistemas hiperbólicos
• Palavras-chave em Inglês: Conservation laws; Riemann problems; hyperbolic systems
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tde/1972

In this dissertation we describe the solutions to the Riemann problem for a system of two conservation laws written in the normal from according to classification of Schaeffer-Shearer in [9]. Through changes of variables Schaeffer-Shearer determined the normal form for a nonlinear system of two conservation laws with an isolated umbilical point in state space. The normal form consists of a system of two equations, with homogeneous and quadratic functions of flow that depend only on two parameters. Also in [9] were established four distinct regions in terms of parameters, denoted by I, II, III and IV, in which varying pair of parameters in each region, the curves of waves that make up the solution of the Riemann problem have the same configuration. In this dissertation we consider the case in which the pair of parameters belongs to region IV, and in the particular case in which one of the parameters is null. In this case, the classic Lax criterion for admissibility of shocks (discontinuity solutions) generally is sufficient to obtain uniqueness of solution. Although, for some initial states, it is necessary to admit in solution also the called compressive shocks, which do not satisfy the Lax criterion.