Long-time behaviour of stochastic Hamilton-Jacobi equations

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  • Authors: Paul Gassiat, Benjamin Gess, Pierre-Louis Lions, Panagiotis E. Souganidis
  • Preprint year: 2022
  • First public date: 2022-11-22
  • arXiv: 2211.12099
  • Status: Published
  • Publication type: Journal article
  • Publication year: 2024
  • Journal: Journal of functional analysis, 286 (2024) 4, p. 110269
  • DOI: 10.1016/j.jfa.2023.110269

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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BibTeX

@article{arxiv221112099,
  title = {Long-time behaviour of stochastic Hamilton-Jacobi equations},
  author = {Paul Gassiat and Benjamin Gess and Pierre-Louis Lions and Panagiotis E. Souganidis},
  year = {2024},
  journal = {Journal of functional analysis, 286 (2024) 4, p. 110269},
  doi = {10.1016/j.jfa.2023.110269},
  eprint = {2211.12099},
  archivePrefix = {arXiv},
  primaryClass = {math.PR}
}

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