Attractors of Reaction Diffusion Systems on Infinite Lattices

Exponential Attractors for Lattice Dynamical Systems in Weighted Spaces

“…For example, the traveling wave solutions were investigated in [12,19,32], the chaotic properties of solutions were examined in [10,11], and the asymptotic behavior of solutions was studied in [1,2,5,7,23,24,27,[29][30][31]. For the study of long-time behavior of partial differential equations on unbounded domain, we refer readers to [3,4,17,25,28].…”

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

“…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.…”

Dynamics of systems on infinite lattices

“…The chaotic properties of solutions were examined by [12,14,15] and the references therein. For the asymptotic behavior of lattice systems, we refer the reader to [6,7,10,23,32].…”

“…The existence of a global attractor for this system was proved in [7] in the standard l 2 space, which does not include traveling wave solutions. The existence of a global attractor in a locally uniform space was showed in [10], which contains traveling wave solutions but is not compact in the topology of the phase space. In this paper, we will prove that the lattice reaction-diffusion system has a global attractor which contains traveling waves as well as is compact in a weighted l 2 space.…”