Asymptotics of the Solutions of the Stochastic Lattice Wave Equation
Asymptotics of the Solutions of the Stochastic Lattice Wave Equation
复制标题
随机格子波方程解的渐近性
DOI：
10.1007/s00205-013-0626-8
复制
发表时间：
2012
影响因子：
2.5
通讯作者：
L. Ryzhik
中科院分区：
文献类型：
--
作者：
T. Komorowski;S. Olla;L. Ryzhik
考虑具有弱随机强迫的离散波动方程解的长时间极限。乘法噪声保存能量，在未固定的情况下也保存动量。我们得到了对平方可积和统计齐次初始数据均成立的极限波函数的时非齐次Ornstein-Uhlenbeck方程。在前一种情况下，界限被理解为点的意义，在后一种情况下，界限被理解为弱的意义。另一方面，平方可积初始数据的弱极限是确定的。
We consider the long time limit for the solutions of a discrete wave equation with weak stochastic forcing. The multiplicative noise conserves energy, and in the unpinned case also conserves momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds for both square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic.