## Section: New Results

### Long-time behavior in scalar conservation laws

Participant : Arnaud Debussche.

In this joint work [23] with J. Vovelle (Université de Lyon 1),
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} , 1p< + . We give a partial result in the general case.