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arXiv · 1310.3779

Invariant measure of scalar first-order conservation laws with stochastic forcing

Arnaud Debussche·Julien Vovelle
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Abstract

Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the invariant measure. Also, since this invariant measure is supported by Lp for some p small, we are led to generalize to the stochastic case the theory of L1 solutions developed by Chen and Perthame in 2003.

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Arnaud Debussche, Julien Vovelle. 2013-10-14. Invariant measure of scalar first-order conservation laws with stochastic forcing. https://arxiv.org/abs/1310.3779

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