Large time behavior of solutions to degenerate parabolic equations with weights

We study the degenerate parabolic equation ∂tu=a(δ(x))upΔu−g(u) in Ω×(0,∞), where Ω⊂RN (N⩾1) is a smooth bounded domain, p⩾1, δ(x)=dist(x,∂Ω) and a is a continuous nondecreasing function such that a(0)=0. Under some suitable assumptions on a and g we prove the existence and the uniqueness of a classical solution and we study its asymptotic behavior as t→∞.