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Structure of the global attractor for a second order strongly damped lattice system. (English) Zbl 1112.37075
Summary: We consider the dynamical behavior of a second-order strongly damped lattice system where the coupled operator is nonnegative definite symmetric. Firstly, we prove the existence of a global attractor, and give an upper bound of Hausdorff dimension of the global attractor, which keeps bounded for large strongly damping. Then, we show that when the damping term is linear and the damping is suitable large, the system has an unbounded one-dimensional global attractor, which is a restricted horizontal curve.
MSC:
37L60Lattice dynamics (infinite-dimensional dissipative systems)
37L30Attractors and their dimensions, Lyapunov exponents
37E45Rotation numbers and vectors