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Dimension of the global attractor for damped nonlinear wave equations |
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| Authors: | Zhou Shengfan |
| Institution: | Department of Mathematics, Sichuan Union University, Chengdu, 610064, People's Republic of China |
| Abstract: | An estimate on the Hausdorff dimension of the global attractor for damped nonlinear wave equations, in two cases of nonlinear damping and linear damping, with Dirichlet boundary condition is obtained. The gained Hausdorff dimension is bounded and is independent of the concrete form of nonlinear damping term. In the case of linear damping, the gained Hausdorff dimension remains small for large damping, which conforms to the physical intuition. |
| Keywords: | Wave equation global attractor Hausdorff dimension |
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