Global well-posedness for strongly damped viscoelastic wave equation |
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| Authors: | Runzhang Xu Yanbing Yang Yacheng Liu |
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| Affiliation: | 1. College of Science , Harbin Engineering University , 150001, People's Republic of China xurunzh@yahoo.com.cn;3. College of Science , Harbin Engineering University , 150001, People's Republic of China |
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| Abstract: | We study the initial boundary value problem for the nonlinear viscoelastic wave equation with strong damping term and dispersive term. By introducing a family of potential wells we not only obtain the invariant sets, but also prove the existence and nonexistence of global weak solution under some conditions with low initial energy. Furthermore, we establish a blow-up result for certain solutions with arbitrary positive initial energy (high energy case) |
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| Keywords: | viscoelastic wave equation global existence blow-up strong damping arbitrary positive initial energy |
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