One-dimensional global attractor for strongly damped wave equations |
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| Affiliation: | 1. College of Science, Guilin University of Technology, Guilin 541004, China;2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;3. School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China;1. University of Memphis, Memphis, TN, United States;2. Polish Academy of Sciences, Warsaw, Poland;3. Oregon State University, Corvallis, OR, United States;1. LMAM, Bat. A, Lorraine-Metz University Ile du Saulcy, 57045 Metz Cedex 01, France;2. King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran 31261, Saudi Arabia |
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| Abstract: | We consider the dynamical behavior of the strongly damped wave equations under homogeneous Neumann boundary condition. By the property of limit set of asymptotic autonomous differential equations, we prove that in certain parameter region, the system has a one-dimensional global attractor, which is a periodic horizontal curve. |
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