On the dimension of the global attractor for a damped semilinear wave equation with critical exponent (Q2738091)
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scientific article; zbMATH DE number 1639267
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the dimension of the global attractor for a damped semilinear wave equation with critical exponent |
scientific article; zbMATH DE number 1639267 |
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On the dimension of the global attractor for a damped semilinear wave equation with critical exponent (English)
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30 August 2001
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Hausdorff dimension
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0.99551404
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0.9709753
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0.96253604
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0.9571153
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0.9527434
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0.9521562
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0.94682735
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0.94431543
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The authors obtain a precise upper bound of the Hausdorff dimension of the global attractor for a damped semilinear wave equation with critical exponent. The obtained Hausdorff dimension decreases as the damping grows and is uniformly bounded for large damping, which conforms to physical intuition. The obtained results generalize and correct the corresponding results obtained recently by \textit{S. Zhou} [J. Math. Phys. 40, No. 3, 1432-1438 (1999; Zbl 0943.35009].
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