Existence result for degenerated parabolic problems in unbounded domains

Abstract

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∗)).