Robust exponential attractors for the strongly damped wave equation with memory. I

We consider the singular limit of the semilinear strongly damped wave equation with memory partial derivative(tt)u - gamma Delta partial derivative(t)u - k(0)Delta u - integral(infinity)(0) k '(s)Delta u(t - s)ds + phi(u) = f, in presence of an arbitrarily growing nonlinearity phi, as the memory kernel k(s) - k(infinity) converges to the Dirac mass at zero. The existence of a robust family of regular exponential attractors is established, under a necessary and sufficient condition on k, along with quantitative estimates of the closeness of the equation with memory to the corresponding limit equation.