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Large deviation principles for first-order scalar conservation laws with stochastic forcing

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arxiv 1806.02955 v4 pith:GRNFMEBJ submitted 2018-06-08 math.PR

Zhao Dong , Jiang-Lun Wu , Rangrang Zhang , Tusheng Zhang This is my paper · ORCID
classification math.PR
keywords conservationfirst-orderlargelawsdeviationkineticprinciplesscalar
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In this paper, we established the Freidlin-Wentzell type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.

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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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