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Item Ondas de Choques Transicionais Para Modelos Quadráticos de Duas Leis de Conservação(Universidade Federal de Goiás, 2007-11-29) ALMEIDA, Gisele Detomazi; MOTA, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539Transitional shock waves arises in solution of initial values problems for non linear systems of conservation laws that are not strictly hyperbolic. These waves are discontinuous solutions that posses viscous profile but do not conform to the Lax characteristic criterion, where inequalities between the shock propagation speed and the characteristic speeds must to be satisfied. These waves arise as transition between wave groups associated with distinct characteristic families. In this work we studied transitional shock waves for a system of two conservation laws with quadratic fux functions and positive defined viscosity matrix. In particular, we studied the transitional shock waves with viscous profile defined by orbits laying on straightlines. We show from examples, for systems with quadratic fux functions and viscosity matrix chosen in a convenience way, that is necessary to use transitional shock waves to solve the Riemann problem (initial data constant by parts) for these systems.Item Problemas Elípticos Assintoticamente Lineares(Universidade Federal de Goiás, 2012-02-02) DAMKE, Caíke da Rocha; SILVA, Edcarlos Domingos da; http://lattes.cnpq.br/7817014732764711In this dissertation we analyze questions of existence and multiplicity of solutions for Dirichlet problem in the asymptotically linear case. To obtain our main results we use variational methods, such as Montain Pass Theorem and Linking Theorem.Moreover, we use the Liapunov-Schmidt reduction.Item Problemas de Riemann para um Sistema Simétrico de Duas Leis de Conservação(Universidade Federal de Goiás, 2010-04-09) LIMA, Lidiane dos Santos Monteiro; MOTA, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539In 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.Item Existência e multiplicidade de soluções de problemas de contorno elípticos de quarta ordem via métodos topológicos(Universidade Federal de Goiás, 2012-02-24) SILVA, Kaye Oliveira da; GONCALVES, Jose Valdo Abreu; http://lattes.cnpq.br/5148611284176776In this work, we employ topological methods in order to study existence and multiplicity of solutions, of nonlinear boundary value problems of the fourth order. More precisely, we make use of results on connected components of fixed points, as well as global bifurcation, to show existence and multiplicity of weak solutions of Partial Differential Equations, involving the Biharmonic operator under Navier boundary conditions. Proofs of the abstract results used, are presented in detail.