Long-time behavior in scalar conservation laws

Arnaud Debussche (1, 2) , Julien Vovelle (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IPSO - Invariant Preserving SOlvers

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.

Mots clés: scalar conservation law; long-time behavior; transport equation

Domaines: Equations aux dérivées partielles [math.AP]

Arnaud Debussche, Julien Vovelle. Long-time behavior in scalar conservation laws. Differential and integral equations, 2009, 22 (3-4), pp.225-238. ⟨hal-00348310⟩