Abstract

This work is concerned with the proof of the existence and uniqueness of the entropy weak solution to the following nonlinear hyperbolic equation: u t + div(vf(u)) = 0 in IR N \Theta [0; T ], with initial data u(:; 0) = u 0 (:) in IR N . where u 0 2 L 1 (IR N ) is a given function, v is a divergence-free bounded function of class C 1 from IR N \Theta [0; T ] to IR N , and f is a function of class C 1 from IR to IR. It also gives a result of convergence of a numerical scheme for the discretization of theis equation. We first show the existence of a "process" solution (which generalizes the concept of entropy weak solutions, and can be obtained by passing to the limit of solutions of the numerical scheme). The uniqueness of this entropy process solution is then proved; it is also proven that the entropy process solution is in fact a entropy weak solution, hence the existence and uniqueness of the entropy weak solution, and the convergence of the numerical scheme. Keywords...

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