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Asymptotic behavior for second order lattice dynamical systems. (English) Zbl 1026.37067

The author considers a spatial disrectization of a scalar damped semilinear wave equation. More precisely a onedimensional lattice dynamical system of diffusively coupled points, each with second order ODE and polynomial nonlinearity (odd with positive coefficients). Using ideas of an earlier paper by the author and other work on first order systems [P. W. Bates, K. Lu, B. Weng, Attractors for lattice dynamical systems, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, No. 1, 143-153 (2001)], the author proves existence of a global attractor.

MSC:

37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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