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 ∂ ttu - γΔ ∂ t u - k (0)Δ u - ∫0∞ {k'} (s)Δ u(t - s)ds + φ (u) = f, in presence of an arbitrarily growing nonlinearity φ, as the memory kernel k(s)-k(∞) 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. © 2008 Pleiades Publishing, Ltd