Approximate dynamics of a class of stochastic wave equations with white noise

This work is concerned with a stochastic wave equation driven by a white noise. Borrowing from the invariant random cone and employing the backward solvability argument, this wave system is approximated by a finite dimensional wave equation with a white noise. Especially, the finite dimension is explicit, accurate and determined by the coefficient of this wave system; and further originating from an Ornstein-Uhlenbek process and applying Banach space norm estimation, this wave system is approximated by a finite dimensional wave equation with a smooth colored noise.