Global attractor for Klein-Gordon-Schrödinger lattice system

Abstract

We considered the longtime behavior of solutions of a coupled lattice dynamical system of Klein-Gordon-Schrödinger equation (KGS lattice system). We first proved the existence of a global attractor for the system considered here by introducing an equivalent norm and using "End Tails" of solutions. Then we estimated the upper bound of the Kolmogorov delta-entropy of the global attractor by applying element decomposition and the covering property of a polyhedron by balls of radii delta in the finite dimensional space. Finally, we presented an approximation to the global attractor by the global attractors of finite-dimensional ordinary differential systems.

Uniform exponential attractors for non-autonomous KGS and Zakharov lattice systems with quasiperiodic external forces

“…For example, the function h m (ω m , u m ) = u m ω m (see [9][10][11][12]) satisfies condition (A1).…”

“…[9][10][11][12][13] and references therein). Yet no result exists on the existence of uniform exponential attractors for these two systems.…”

Uniform attractors for non-autonomous Klein-Gordon-Schrödinger lattice systems

“…For example, Abdallah [15] , Yin et al [16] , and Zhao and Zhou [17] investigated the existence, upper semicontinuity, and Kolmogorov entropy of global attractors/compact kernel sections for autonomous/nonautonomous KGS lattice systems, respectively. In this paper, we study the existence, an upper bound of the Kolmogorov entropy, and an upper semicontinuity of compact uniform attractor for a family of processes corresponding to the following non-autonomous KGS lattice system:…”

Attractors of the Klein-Gordon-Schrödinger lattice systems with almost periodic nonlinear part

“…The asymptotic behavior for different types of Klein-Gordon-Schrödinger autonomous and non-autonomous LDSs with nonlinear part of the form f (u, v) has been studied, cf. [1,4,23,29,30,37,38,42], and the existence of the uniform global attractor for a family of first order, second order, and FitzHugh-Nagumo non-autonomous LDSs with nonlinear part of the form f (u, t) has been studied in [2,3,10]. Here we carefully investigate the existence of the uniform global attractor for the following family of Klein-Gordon-Schrödinger non-autonomous LDSs with nonlinear part of the form f (u, v, t) such that for j ∈ Z n , t > τ , and τ ∈ R, i • u j − (Au) j + iαu j + f j (u j , v j , t) = g j (t) ,…”