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 …

This paper is devoted to existence, uniqueness and asymptotic behavior, as time tends to
infinity, of the solutions of an integro-partial differential equation arising from the theory of …

In gradient-like systems, the limit set of an orbit belongs to the set of equilibrium points. We
give easily applied conditions to determine when this limit set is a single point. Applications …

We present a new method of investigating the so-called quasi-linear strongly-damped wave
equations in bounded 3D domains. This method allows us to establish the existence and …

A strongly damped semilinear wave equation on the whole space is considered. Existence
and uniqueness results are provided, together with the existence of an absorbing set, which …

The authors consider non-autonomous dynamical behaviour of wave-type evolutionary
equations with nonlinear damping and critical nonlinearity. These type of waves equations …

A strongly damped semilinear wave equation with linear memory is considered in a history
space setting. Namely, the evolution of the past history of the displacement vector is …

We consider an integro-partial differential equation of hyperbolic type with a cubic
nonlinearity, in which no dissipation mechanism is present, except for the convolution term …

Two types of second-order in time partial differential equations, namely semilinear wave
equations and semilinear beam equations are considered. To solve these equations with …