Viscous scalar conservation law with stochastic forcing: strong solution and invariant measure

Abstract : We are interested in viscous scalar conservation laws with a white-in-time but spatially correlated stochastic forcing. The equation is assumed to be one-dimensional and periodic in the space variable, and its flux function to be locally Lipschitz continuous and have at most polynomial growth. Neither the flux nor the noise need to be non-degenerate. In a first part, we show the existence and uniqueness of a global solution in a strong sense. In a second part, we establish the existence and uniqueness of an invariant measure for this strong solution.
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https://hal.archives-ouvertes.fr/hal-02133338
Contributeur : Sofiane Martel <>
Soumis le : samedi 18 mai 2019 - 00:30:31
Dernière modification le : mercredi 5 juin 2019 - 17:01:48

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  • HAL Id : hal-02133338, version 1
  • ARXIV : 1905.07908

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Sofiane Martel, Julien Reygner. Viscous scalar conservation law with stochastic forcing: strong solution and invariant measure. 2019. ⟨hal-02133338⟩

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