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.
Robust exponential attractors for the strongly damped wave equation with memory. i / Di Plinio, F.; Pata, V.. - In: RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 1061-9208. - 15:3(2008), pp. 301-315. [10.1134/S1061920808030014]
Robust exponential attractors for the strongly damped wave equation with memory. i
Di Plinio F.;
2008
Abstract
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.File | Dimensione | Formato | |
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