Existence and uniqueness of invariant measures are claimed for anisotropic degenerate parabolic-hyperbolic conservation laws driven by additive white noise, extending Debussche-Vovelle's first-order theory.
On stochastic conservation laws and Malliavin calculus
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abstract
For stochastic conservation laws driven by a semilinear noise term, we propose a generalization of the Kru\v{z}kov entropy condition by allowing the Kru\v{z}kov constants to be Malliavin differentiable random variables. Existence and uniqueness results are provided. Our approach sheds some new light on the stochastic entropy conditions put forth by Feng and Nualart [J. Funct. Anal., 2008] and Bauzet, Vallet, and Wittbold [J. Hyperbolic Differ. Equ., 2012].
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2019 1verdicts
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Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing
Existence and uniqueness of invariant measures are claimed for anisotropic degenerate parabolic-hyperbolic conservation laws driven by additive white noise, extending Debussche-Vovelle's first-order theory.