Parabolic double phase obstacle problems

We prove existence results for the parabolic double phase obstacle problem: Find u is an element of K subset of 0 with u(., 0) = 0 satisfying 0 is an element of u(t) + Au + F(u) + partial derivative I-K(u) in X-0*, where A : X-0 -> X-0* given by Au := - div ( |del u|(P-2)del u + mu(x)|del u|(q-2)del u) for u is an element of X-0, is the double phase operator acting on X-0 = L-p(0, tau; W-0(1, H) (Omega) with W-0(1, H)(Omega) denoting the associated Musielak-Orlicz Sobolev space with generalized homogeneous boundary values. The obstacle is represented by the closed convex set k with the obstacle function psi through K = {v is an element of X-0 : v(x, t) <= psi(x, t) for a.a. (x, t) is an element of = Omega x (0, tau)} and I-K is the indicator function related to K with partial derivative I-K denoting its subdifferential in the sense of convex analysis.