%0 Journal Article
%T Long-time behavior in scalar conservation laws
%A Arnaud Debussche
%A Julien Vovelle
%J Mathematics
%D 2008
%I arXiv
%X 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 $L^{p}$, $1\leq p<+\infty$. We give a partial result in the general case.
%U http://arxiv.org/abs/0812.3537v1