Convergence of a Finite Volume Scheme for Compactly Heterogeneous Scalar Conservation Laws
Résumé
We build a finite volume scheme for the scalar conservation law
$\p_t u + \p_x (H(x, u)) = 0$ with initial condition $u_o \in \L{\infty}(\R, \R)$
for a wide class of flux function $H$, convex with respect to the second variable.
The main idea for the construction of the scheme is to use the theory of
discontinuous flux. We prove that the resulting approximating sequence converges in
$\Lloc{p}(]0,+\infty[ \times \R, \R)$, $p \in [1, +\infty[$, to the entropy
solution.
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