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Long-time behavior, invariant measures and regularizing effects for stochastic scalar conservation laws

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arxiv 1411.3939 v3 pith:SLLHKFOL submitted 2014-11-14 math.AP math.PR

Benjamin Gess , Panagiotis E. Souganidis This is my paper · ORCID
classification math.APmath.PR
keywords conservationlawsscalarbehaviorinvariantlong-timepathwiseregularization
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We study the long-time behavior and the regularity of pathwise entropy solutions to stochastic scalar conservation laws with random in time spatially homogeneous fluxes and periodic initial data. We prove that the solutions converge to their spatial average, which is the unique invariant measure, and provide a rate of convergence, the latter being new even in the deterministic case for dimensions higher than two. The main tool is a new regularization result in the spirit of averaging lemmata for scalar conservation laws, which, in particular, implies a regularization by noise-type result for pathwise quasi-solutions.

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  1. Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

    math.AP 2019-08 reject novelty 6.0 of 10

    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.

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