| Global Attractor for Damped Wave Equations with Nonlinear Memory |
| Received:March 24, 2010 Revised:April 18, 2011 |
| Key Words:
global attractor nonlinear memory term damped wave equation.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10471018). |
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| Abstract: |
| Let $\Omega\subset{\Bbb{R}}^{n}$ be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term $$u_{tt}+\alpha u_{t} -\Delta u - \int_{0}^{t}\mu (t-s)|u(s)|^{\beta} u(s)\d s + g(u)=f.$$ Based on a time-uniform priori estimate method, the existence of the compact global attractor is proved for this model in the phase space ${H_{0}^{1}(\Omega) \times L^{2}(\Omega)}$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.02.009 |
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