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A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem

✍ Scribed by Miroslav Bulíček; Dalibor Pražák

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
314 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

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.

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