Abstract

In this paper we consider the nonlinear degenerate evolution equation with strong damping,(*)      {K(x,t)utt−Δu−Δut+F(u)=0   in   Q=Ω×]0,T[u(x,0)=u0,   (ku′)(x,0)=0   in   Ωu(x,t)=0           on   ∑=Γ×]0,T[where K is a function with K(x,t)≥0, K(x,0)=0 and F is a continuous real function satisfying(**)     sF(s)≥0,   for   all   s∈R,             Ω is a bounded domain of Rn, with smooth boundary Γ. We prove the existence of a global weak solution for (*).