Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

Gui-Qiang G. Chen; Peter H. C. Pang

doi:10.1007/s11401-019-0169-x

Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (6) : 967 -1004. DOI: 10.1007/s11401-019-0169-x

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Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

Gui-Qiang G. Chen ¹^,^a
, Peter H. C. Pang ¹^,^b

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Abstract

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white noises. Some further developments, problems, and challenges in this direction are also discussed.

Keywords

Stochastic solutions / Entropy solutions / Invariant measures / Existence / Uniqueness / Stochastic forcing / Anisotropic degenerate / Parabolichyperbolic equations / Long-time behavior

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Gui-Qiang G. Chen, Peter H. C. Pang. Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing. Chinese Annals of Mathematics, Series B, 2019, 40(6): 967-1004 DOI:10.1007/s11401-019-0169-x