# Long-time behavior in scalar conservation laws

1 IRMAR - Institut de Recherche Mathématique de Rennes 2 IPSO - Invariant Preserving SOlvers IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique

Abstract : We consider the long-time behavior of the entropy solution of a first-order scalar conservation law on a Riemannian manifold. In the case of the Torus, we show that, under a weak property of genuine non-linearity of the flux, the solution converges to its average value in $L^{p}$, \$1\leq p

Author: Arnaud Debussche - Julien Vovelle -

Source: https://hal.archives-ouvertes.fr/