Long-time behavior of stochastic Hamilton-Jacobi equations
Long-time behavior of stochastic Hamilton-Jacobi equations
复制标题
随机 Hamilton-Jacobi 方程的长期行为
DOI：
10.1016/j.jfa.2023.110269
复制
发表时间：
2024
影响因子：
1.7
通讯作者：
Souganidis, Panagiotis E.
中科院分区：
文献类型：
--
作者：
Gassiat, Paul;Gess, Benjamin;Lions, Pierre-Louis;Souganidis, Panagiotis E.
分析了随机Hamilton-Jacobi方程的长时间行为，包括作为特例的随机平均曲率流。在各种设置中，可以获得新的和锐化的结果。其中包括(I)具有均匀噪声的平均曲率流的噪声正则化，它证明了噪声的加入加速了解的衰减，以及(Ii)空间非齐次随机Hamilton-Jacobi方程解的长时间收敛。附录中给出了一些关于非线性随机偏微分方程解的实例。
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.