Long-time behavior in scalar conservation laws

2008/12/18 by Arnaud Debussche, Debussche, Arnaud, Julien Vovelle +1
Mathematics · #35B40 #35L65 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35L65

paper · pdf · doi:10.48550/arxiv.0812.3537

arxiv created 2008/12/18 · arxiv updated 2009/12/01

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≤ p<+∞. We give a partial result in the general case.

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