Preprint C31/2004
Problema de Riemann para Duas Leis de Conservação do Tipo IV com Região Elíptica
Vítor Matos
Keywords: Conservation laws | Riemann problem | elliptic region | global non-existence | non-classical rarefaction wave | travelling-wave
On this thesis we obtained essentially three kinds of results. First we obtain general results on two conservation laws used in a practical method for Riemann Problems solving. Also we study a quadratic model of two Conservation Laws of type IV with elliptic region. We solve the Riemann Problem with Lax?s entropy criterion. Then we prove the existence of a Hopf bifurcation that implies non-existence of a travelling-wave for several solutions, even with both states in the strictly hyperbolic region. Finally we perform numerical simulations for pairs of states without solution and we find long lasting solutions, which, we believe, fail to be asymptotic solutions. However more numerical simulations are needed in order a best understanding of these numerical results.