Initial boundary value problem for a class of fourth-order wave equation with viscous damping term |
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| Authors: | Runzhang Xu Shuo Wang Yanbing Yang Yunhua Ding |
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| Institution: | 1. College of Science , Harbin Engineering University , Harbin 150001 , People's Republic of China xurunzh@yahoo.com.cn;3. College of Automation , Harbin Engineering University , Harbin 150001 , People's Republic of China;4. College of Science , Harbin Engineering University , Harbin 150001 , People's Republic of China |
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| Abstract: | In this article we study the initial boundary value problem for a class of fourth-order nonlinear wave equation with viscous damping term u tt ???αu xxt ?+?u xxxx ?=?f(u x ) x . By argument related to the potential well-convexity method, we prove the global existence and nonexistence of the solution. Further, we give some sharp conditions for global existence and nonexistence of the solution. This generalizes the results obtained in Chen and Lu G. Chen and B. Lu, The initial-boundary value problems for a class of nonlinear wave equations with damping term, J. Math. Anal. Appl. 351 (2009), pp. 1–15]. |
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| Keywords: | fourth-order nonlinear wave equation viscous damping global existence nonexistence potential well |
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