Abstract
In this paper we study the asymptotic behavior of solutions of the following nonautonomous wave equation with nonlinear dissipation.
{u(tt) + vertical bar u(t)vertical bar(alpha)u(t) - Delta u + f(u) = g (t,x), in R(+) C Omega, u(t,x) = 0, on R(+) X partial derivative(Omega,) where f is an analytic function, alpha is a small positive real and g(t, center dot) tends to 0 sufficiently fast in L (2)(Omega) as t tends to a.
We also obtain a general convergence result and the rate of decay of solutions for a class of second order ODE containing as a special case
{U(t) + parallel to U(t) parallel to(alpha) U(t) + del F(U(t)) = g(t), t epsilon R(+) , U(0) = U(0) epsilon R(N,) U(0)=U(1 epsilon)R(N.)