Speed of propagation for Hamilton–Jacobi equations with multiplicative rough time dependence and convex Hamiltonians
Speed of propagation for Hamilton–Jacobi equations with multiplicative rough time dependence and convex Hamiltonians
复制标题
具有乘法粗糙时间依赖性和凸哈密顿量的 Hamilton-Jacobi 方程的传播速度
DOI：
10.1007/s00440-019-00921-5
复制
发表时间：
2018
影响因子：
2
通讯作者：
P. Souganidis
中科院分区：
文献类型：
--
作者：
Paul Gassiat;B. Gess;P. Lions;P. Souganidis
我们证明了具有乘性、粗时间依赖性、典型的随机和凸哈密顿量的Hamilton-Jacobi方程的初值问题满足有限传播速度。我们证明了在一般情况下，依赖范围是由路径的“骨架”的长度的倍数所限定的，即通过连接原始路径的连续极值而得到的分段线性路径。当驱动路径为布朗运动时，我们证明了它的骨架几乎肯定是有限长的。我们还讨论了估计的最优性。
We show that the initial value problem for Hamilton–Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed of propagation. We prove that in general the range of dependence is bounded by a multiple of the length of the “skeleton” of the path, that is a piecewise linear path obtained by connecting the successive extrema of the original one. When the driving path is a Brownian motion, we prove that its skeleton has almost surely finite length. We also discuss the optimality of the estimate.
影响因子：
3
作者：
Gess, Benjamin;Souganidis, Panagiotis E.
通讯作者：
Souganidis, Panagiotis E.