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Zbl 1179.37104
Bul{\'\i}ček, Miroslav; Pražák, Dalibor
A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem. (English)
[J] Appl. Math. Lett. 22, No. 7, 1025-1028 (2009). ISSN 0893-9659

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 2000:: *37L30 Attractors and their dimensions

Keywords: nonlinear hyperbolic problem; dimension of attractor; fractal dimension; squeezing property; method of $\ell $-trajectories

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