Leis de conservação: teoria geral

• Autor(a) principal: Viana, Matheus Magaiver Barbosa
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/15864
• topic: EDP; EDP quasilinear de primeira ordem; Características; Solução generalizada; Onda de choque; Onda de rarefação; Condição de admissibilidade; Entropia; Problema de Riemann; PDE; First-order quasilinear PDE; Characteristics; Generalized solution; Shock wave; Rarefaction wave; Admissibility condition; Entropy; Riemann problem; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE

In this thesis we study some aspects of the theory of Partial Differential Equations (PDE's), the theory of the existence and the uniqueness of classical solutions to the Cauchy problem u_t+f'(u)u_x=0, u(0,x)=u_0(x) in the range Π_T=[0,T)xR, where f∈C²(R) and u_0∈C¹(R). Furthermore, we will show some results on generalized solutions and build a generalized solution for functions f(u)=u³ and f(u)=sen u, both with five discontinuities lines. Next, some notions of Kruzhkov's generalized entropy solution are presented. Finally, we will discuss the solutions of the Riemann problem for a concave or convex function f and how concave or convex envelopes allow us to solve the Riemann problem for a function f∈C¹(R).