Uniqueness for stochastic non-linear wave equations

作者：Ondrejat Martin^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2007, 67(12): 3287-3310.

DOI：10.1016/j.na.2006.10.012

• stochastic wave equation

We prove uniqueness of solutions of the equation u(tt) = Delta u + f(u) + g(u) W, u(0) = u(0,) u(t)(0) =v(0) on R-d in the class of processes with paths in H-1. Here (u(0), v(0)) is a random variable in H1 circle plus L-2, W is a spatially homogeneous Wiener process with finite spectral measure, and f, g are locally Lipschitz functions of subcritical growth.

• 出版日期2007-12-15