The authors consider abstract nonlinear second order evolution equations with a nonlinear
damping. Questions related to long time behavior, existence and structure of global …

The existence of a global attractor in the natural energy space is proved for the semilinear
wave equation utt+ βut−∆ u+ f (u)= 0 on a bounded domain Ω⊂ Rn with Dirichlet boundary …

We prove the existence of the universal attractor for the strongly damped semilinear wave
equation, in the presence of a quite general nonlinearity of critical growth. When the …

Smooth attractors for strongly damped wave equations Page 1 Nonlinearity Smooth attractors for
strongly damped wave equations To cite this article: Vittorino Pata and Sergey Zelik 2006 …

The energy-equation approach used to prove the existence of the global attractor by
establishing the so-called asymptotic compactness property of the semigroup is considered …

We continue the analysis on the model equation arising in the theory of viscoelasticity
$$\partial_ {tt} u (t)-\big [1+ k_t (0)\big]\Delta u (t)-\int_0^\infty k'_t (s)\Delta u (ts)\ds+ f (u (t)) …

A semilinear strongly damped wave equation with memory is considered in the past history
framework. The existence of global attractors of optimal regularity is established, both for …

An improvement in the original constructions of exponential attractors is indicated. Namely,
when the solution semigroup is α-contractive and satisfies the discrete squeezing property …

STRONGLY DAMPED WAVE EQUATIONS ON R3 WITH CRITICAL NONLINEARITIES Page 1
Communications in Applied Analysis 9 (2005), no. 2, 161–176 STRONGLY DAMPED WAVE …

We prove the existence of a compact global attractor for the Navier-Stokes equations of
compressible flow in one space dimension, and we estimate the number of its determining …