Compact uniform attractors for dissipative non-autonomous lattice dynamical systems

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

“…(11) and (H3) imply that −Cφ + F (φ) + Σ(t) is locally Lipschitz continuous from H β × R into H β w. r. t. φ ∈ H β and Hölder continuous in t on interval [τ, τ + T ] (T > 0). The proof is completed by the classical theory of operator semigroup in Chapter 6 of Ref.…”

“…From Chepyzhov and Vishik [14] , we know that kernel sections and uniform attractors are two important concepts in describing the long time behavior of non-autonomous dynamical systems. Many authors [8][9][10][11][12] investigated the compact kernel sections or compact uniform attractors of non-autonomous LDSs.…”

“…The lattice dynamical system (LDS), one of infinite dimensional dynamical systems, attracts more and more researchers [1][2][3][4][5][6][7][8][9][10][11][12][13] due to its wide application in many fields, such as chemical reaction theory, biology, laser systems, material science, electrical engineering, etc. From Chepyzhov and Vishik [14] , we know that kernel sections and uniform attractors are two important concepts in describing the long time behavior of non-autonomous dynamical systems.…”

“…[11], the existence of the uniform attractor is obtained. The structure of A H(Σ0) can be directly obtained by Chepyzhov and Vishik [14] .…”

Uniform Attractor for the Partly Dissipative Nonautonomous Lattice Systems

“…Authors in 18, 19 also prove that the uniform smallness of solutions of autonomous infinite lattice systems for large space and time variables is sufficient and necessary conditions for asymptotic compactness of it. Recently, "tail ends" method is extended to non-autonomous infinite lattice systems; see [20][21][22] . The traveling wave solutions of lattice differential equations are studied in 23-25 .…”