Homogenization of a stochastically forced Hamilton-Jacobi equation |
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| Authors: | Benjamin Seeger |
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| Institution: | 1. Laboratoire Jacques-Louis Lions and Centre National de la Recherche Scientifique, Sorbonne Université, 4 Place Jussieu, 75252 Paris, France;2. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, PR China;1. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;2. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China;1. Department of Mathematics, University of Trento, Via Sommarive 14, 38123 Povo (TN), Italy;2. University of Bonn, Institute for Applied Mathematics, Endenicher Allee 60, 53115 Bonn, Germany |
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| Abstract: | We study the homogenization of a Hamilton-Jacobi equation forced by rapidly oscillating noise that is colored in space and white in time. It is shown that the homogenized equation is deterministic, and, in general, the noise has an enhancement effect, for which we provide a quantitative estimate. As an application, we perform a noise sensitivity analysis for Hamilton-Jacobi equations forced by a noise term with small amplitude, and identify the scaling at which the macroscopic enhancement effect is felt. The results depend on new, probabilistic estimates for the large scale Hölder regularity of the solutions, which are of independent interest. |
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| Keywords: | Stochastic homogenization Stochastic Hamilton-Jacobi equation Stochastic enhancement Eikonal equation |
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