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A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem. (English) Zbl 1179.37104
Summary: We study a semilinear hyperbolic problem, written as a second-order evolution equation in an infinite-dimensional Hilbert space. Assuming existence of the global attractor, we estimate its fractal dimension explicitly in terms of the data. Despite its elementary character, our technique gives reasonable results. Notably, we require no additional regularity, although nonlinear damping is allowed.
MSC:
37L30Attractors and their dimensions, Lyapunov exponents
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