Smoluchowski-Kramers approximation for a general class of SPDE's

differential equations perturbed by a non-Gaussian noisy term. Namely, we show that the solution of the one-dimensional semi-linear stochastic damped wave equations μμtt(t, x)+ut(t, x) = Δu(t, x)+b(x, u(t, x))+g(x, u(t, x))ẇ(t), u(0) = o0, ut (0) = υ0, endowed with Dirichlet boundary conditions, converges as the parameter μ goes to zero to the solution of the semi-linear stochastic heat equation ut(t, x) = Δu(t, x) + b(x, u(t, x)) + g(x, u(t, x))ẇ(t), u(0) = u0, endowed with Dirichlet boundary conditions.