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arXiv · 0812.3537

Long-time behavior in scalar conservation laws

Arnaud Debussche·Julien Vovelle
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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 $L^{p}$, $1\leq p<+\infty$. We give a partial result in the general case.

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Arnaud Debussche, Julien Vovelle. 2008-12-18. Long-time behavior in scalar conservation laws. https://arxiv.org/abs/0812.3537

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