Strongly nonlinear parabolic equations with natural growth in general domains

In this paper, we deal with the existence and boundedness of solutions for nonlinear parabolic problem whose model is {partial derivative u(t) - Delta(p)u + mu|u|(p-2) u = L(x, t, u) in Omega x (0, T), u(x, t) = 0 on partial derivative Omega x (0, T), u(x, 0) = u(0) in Omega, where Omega is unbounded domain, L(x, t, del u) = d(x, t)|del u|(p) + f (x, t) - div g(x, t), T is a positive number, 1 < p < N, d is an element of L-infinity (Omega x(0, T)), Delta(p)u is the p-Laplace operator and the lower order terms have a power growth of order p with respect to del u. The assumptions on the source terms lead to the existence results though with exponential integrability.