Attractors for partly dissipative lattice dynamic systems in weighted spaces |
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Authors: | Xiao-jun Li Da-bin Wang |
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Affiliation: | a School of Science, Hohai University, Nanjing, Jiangsu 210098, China b Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China |
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Abstract: | In this paper, we study the asymptotic behavior of solutions for the partly dissipative lattice dynamical systems in weighted spaces. We first establish the dynamic systems on infinite lattice, and then prove the existence of the global attractor in weighted spaces by the asymptotic compactness of the solutions. It is shown that the global attractors contain traveling waves. The upper semicontinuity of the global attractor is also considered by finite-dimensional approximations of attractors for the lattice systems. |
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Keywords: | Lattice system Global attractor Weighted space Asymptotic compactness Approximation |
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