Stable and unstable sets for the Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms |
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| Institution: | 1. Department of Applied Mathematics, Zhejiang University of Technology, 310032, Hangzhou, PR China;2. School of Mathematical Science, Peking University, 100871, Beijing, PR China;1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, PR China;2. Department of Applied Mathematics, Taiyuan University of Science and Technology, 030024 Taiyuan, PR China;1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, People’s Republic of China;2. Department of Mathematics and Statistics, Curtin University, Perth, WA6845, Australia;1. Department of Mathematics & Computer Science, Laurentian University, Sudbury, P3E 2C6 Ontario, Canada;2. School of Mathematics and Physics, Queen''s University Belfast, University Road, Belfast BT7 1NN, United Kingdom |
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| Abstract: | For the Cauchy problem for the nonlinear wave equation with nonlinear damping and source terms we define stable and unstable sets for the initial data. We prove that, if during the evolution the solution enters into the stable set, the solution is global and we are able to estimate the decay rate of the energy. If during the evolution the solution enters into the unstable set, the solution blows up in finite time. |
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