Existence of global bounded weak solutions to systems of Keyfitz-Kranzer type with a source

Abstract

En esta tesis probamos la existencia de solución débil para dos problemas de Cauchy asociados con sistemas 2 × 2 de tipo Keyfitz-Kranzer con ciertos términos fuente y valores iniciales acotados y medibles. Uno es un sistema de tipo Keyfitz-Kranzer simétrico y el otro es el modelo Aw-Rascle para flujo de tráfico el cual es un sistema de tipo Keyfitz-kranzer no simétrico. Para esto, en ambos casos, obtenemos una L1(R) estimativa relacionada con uno de los invariantes de Riemann, entonces usando esta estimativa aplicamos el método de la compacidad compensada para probar la convergencia puntual de las soluciones viscosas. Para los problemas anteriores en ausencia de términos fuente obtenemos como un caso particular la existencia de solución débil entrópica. Finalmente estudiamos un sistema (n + 1) × (n + 1) de tipo keyfitz-kranzer no simétrico con un término fuente particular. / Abstract. In this thesis we prove the existence of a weak solution for two Cauchy problems associated with 2 × 2 systems of Keyfitz-Kranzer type with certain source terms and bounded measurable initial data. One is a symmetric system of Keyfitz-Kranzer type and the other is the Aw-Rascle model for traffic flow which is a non-symmetric system of Keyfitz-Kranzer type. For it, in both cases, we obtain an estimate in L1(R) related to one of the Riemann invariants, then using this estimate we apply the compensated compactness method to prove the pointwise convergence of the viscosity solutions. For the above problems in the absence of source terms we obtain as a particular case the existence of weak entropy solution. Finally we study a (n+1)×(n+1) non-symmetric system of Keyfitz-Kranzer type with a particular source term (Texto tomado de la fuente).

In this thesis we prove the existence of a weak solution for two Cauchy problems associated with 2 × 2 systems of Keyfitz-Kranzer type with certain source terms and bounded measurable initial data. One is a symmetric system of Keyfitz-Kranzer type and the other is the Aw-Rascle model for traffic flow which is a non-symmetric system of Keyfitz-Kranzer type. For it, in both cases, we obtain an estimate in L 1 (R) related to one of the Riemann invariants, then using this estimate we apply the compensated compactness method to prove the pointwise convergence of the viscosity solutions. For the above problems in the absence of source terms we obtain as a particular case the existence of weak entropy solution. Finally we study a (n+ 1)×(n+ 1) non-symmetric system of Keyfitz-Kranzer type with a particular source term.