Viscous scalar conservation law with stochastic forcing: strong solution and invariant measure - Archive ouverte HAL Access content directly
Journal Articles Nonlinear Differential Equations and Applications Year : 2020

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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Dates and versions

hal-02133338 , version 1 (18-05-2019)
hal-02133338 , version 2 (24-04-2020)

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Cite

Sofiane Martel, Julien Reygner. Viscous scalar conservation law with stochastic forcing: strong solution and invariant measure. Nonlinear Differential Equations and Applications, 2020, 27, pp.34. ⟨10.1007/s00030-020-00637-9⟩. ⟨hal-02133338v2⟩
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