ABSTRACT
Introduction Let Ω be a bounded domain in Rn with a smooth boundary Γ. In this article we study the solvability and long-time behavior of the following initial-boundary value problem:
utt −∆u+ |u|k∂j(ut) = |u|p−1u, in Ω× (0, T ) ≡ QT ,
u(x, 0) = u0(x) ∈ H10 (Ω), ut(x, 0) = u1(x) ∈ L2(Ω), (1)
u = 0, on Γ× (0, T ), where j(s) is a continuous, convex real valued function defined on R and ∂j is its sub-differential (see [4]).
