Long-time behaviour of stochastic Hamilton-Jacobi equations

Paul Gassiat; Benjamin Gess; Pierre-Louis Lions; Panagiotis E. Souganidis

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arXiv · 2211.12099

Long-time behaviour of stochastic Hamilton-Jacobi equations

Paul Gassiat·Benjamin Gess·Pierre-Louis Lions·Panagiotis E. Souganidis

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Abstract

The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature flow as a special case. In a variety of settings, new and sharpened results are obtained. Among them are (i) a regularization by noise phenomenon for the mean curvature flow with homogeneous noise which establishes that the inclusion of noise speeds up the decay of solutions, and (ii) the long-time convergence of solutions to spatially inhomogeneous stochastic Hamilton-Jacobi equations. A number of motivating examples about nonlinear stochastic partial differential equations are presented in the appendix.

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Paul Gassiat, Benjamin Gess, Pierre-Louis Lions, Panagiotis E. Souganidis. 2022-11-22. Long-time behaviour of stochastic Hamilton-Jacobi equations. https://arxiv.org/abs/2211.12099

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