论文标题
随机汉密尔顿 - 雅各比方程的长期行为
Long-time behaviour of stochastic Hamilton-Jacobi equations
论文作者
论文摘要
随机汉密尔顿 - 雅各比方程的长期行为进行了分析，包括随机平均曲率流作为特殊情况。在各种环境中，获得了新的和锐利的结果。其中包括（i）通过噪声现象的正则化，用于平均曲率流的均匀噪声，这表明包含噪声会加速溶液的衰减，以及（ii）溶液与空间不均匀的随机型汉密尔顿 - 雅各布方程的长期收敛。附录中介绍了许多有关非线性随机偏微分方程的激励示例。
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.
