Existence result for degenerated parabolic problems in unbounded domains

摘要

In this paper, we study the existence of solutions for strongly nonlinear degenerated parabolic problem ?u/?t?diva(x,t,u,?u)+g(x,t,u,?u) = f, in unbounded domains O, where A is a classical divergence operator of Leray-Lions acting from Lp(0,T,W1,p 0(O,w)) to its dual, while g(x,t,s,ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s and f ∈ Lp0(0,T,W?1,p0(O,w?)).