Long-time behavior of stochastic Hamilton-Jacobi equations

Long-time behavior of stochastic Hamilton-Jacobi equations

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 homog...

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Veröffentlicht in:Journal of functional analysis 2024-02, Vol.286 (4), p.110269, Article 110269
Hauptverfasser: Gassiat, Paul, Gess, Benjamin, Lions, Pierre-Louis, Souganidis, Panagiotis E.
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Sprache:eng
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Mathematics
Probability
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container_title Journal of functional analysis
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creator Gassiat, Paul
Gess, Benjamin
Lions, Pierre-Louis
Souganidis, Panagiotis E.
description 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.
doi_str_mv 10.1016/j.jfa.2023.110269
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title Long-time behavior of stochastic Hamilton-Jacobi equations
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