Weak solutions for a doubly degenerate quasilinear parabolic equation with random forcing

We investigate the problem of existence of a probabilistic weak solution for the initial boundary value problem for the model doubly degenerate stochastic quasilinear parabolic equation [GRAPHICS] where W is a d-dimensional Wiener process defined on a complete probability space, f is a vector-function, p, alpha, mu are some non negative numbers satisfying appropriate restrictions. The equation arises from a suitable stochastic perturbation of the Darcy Law in the motion of an ideal barotropic gas.