A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem |
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Authors: | Miroslav Bulí?ek Dalibor Pra?ák |
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Institution: | 1. Mathematical Institute, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic;2. Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic |
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Abstract: | 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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