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Journal Articles Probability Theory and Related Fields Year : 2015

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

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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Dates and versions

hal-00872657 , version 1 (14-10-2013)
hal-00872657 , version 2 (22-03-2019)

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Arnaud Debussche, Julien Vovelle. Invariant measure of scalar first-order conservation laws with stochastic forcing. Probability Theory and Related Fields, 2015, 163 (3-4), pp.575-611. ⟨10.1007/s00440-014-0599-z⟩. ⟨hal-00872657v2⟩
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