Long-time behavior in scalar conservation laws

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

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.

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