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Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

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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.

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  1. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK

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

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  1. Gui-Qiang G. Chen
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Correspondence to Gui-Qiang G. Chen or Peter H. C. Pang.

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Dedicated to Professor Andrew J. Majda on the occasion of his 70th birthday

This work was supported by the UK Engineering and Physical Sciences Research Council Award EP/E035027/1, EP/L015811/1, the Royal Society-Wolfson Research Merit Award (UK) and an Oxford Croucher Scholarship

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Chen, GQ.G., Pang, P.H.C. Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing. Chin. Ann. Math. Ser. B 40, 967–1004 (2019). https://doi.org/10.1007/s11401-019-0169-x

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