Pullback Attractors for a Damped Semilinear Wave Equation with Delays |
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Authors: | Kai Xuan Zhu Yong Qin Xie Feng Zhou |
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Institution: | 1. Hu'nan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone;2. College of Mathematics and Computational Science, Hu'nan University of Arts and Science, Changde 415000 P. R. China;3. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114 P. R. China;4. College of Science, China University of Petroleum(East China), Qingdao 266580, P. R. China |
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Abstract: | In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g(t, u t ) may be driven by a function with very weak assumptions, namely, just measurability. We analyze the well-posedness of solutions and verify the existence of the pullback D-attractor in \({C_{H_0^1\left( \Omega \right)}} \times {C_{{L^2}\left( \Omega \right)}}\) by constructing the energy functional and combining with the idea of the contractive function. |
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Keywords: | Wave equations critical nonlinearity delays pullback attractors |
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