Attractors for a class of autonomous wave equations of the Klein-Gordon-Zakharov type

Abstract

This work investigates the long-time dynamics of an autonomous coupled Klein-Gordon-Zakharov type wave system defined on a bounded smooth domain in Rn, for n ≥ 3. We establish global well-posedness of solutions in a suitable phase space by employing semigroup theory and we proceed to derive the dissipative properties required in order to construct the associated dynamical system. The asymptotic behavior is then analyzed in detail. We prove the existence of a global attractor, we study some properties for it, such as regularity and upper semicontinuity, and we show that it possesses finite fractal dimension. We also construct exponential attractors for the semigroup generated by the wave system through two different approaches.