Resolução do problema de Riemann através de um método variacional

Abstract

The balance laws express in a more general way the conservation laws and therefore it is naturalthattheycoincideinsomedefinitionsorresultsthatwewillshowhere. Thestrictly hyperbolic systems of conservation laws in a spatial dimension under certain conditions is a symmetrizable system, therefore it has a convex entropy. This induces to define the entropy-entropy flux pair and the entropy production, minimum ingredients to use the Entropy rate admissibility criterion and check whether the solution of the respective Riemann problem is optimal. The entropy rate defined here in terms of entropy is a functional that can be minimized in the wave fans with constant states of the Riemann problem using the Euler-Lagrange equations, we show that the solutions of the Riemann problem are functions of bounded variation, resulting in a variational method to solve the respective problem. In this work it will be shown that the solution obtained by the variational method, coincides with the solution obtained by the method of characteristics.