Global well‐posedness for strongly damped multidimensional generalized Boussinesq equations |
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| Authors: | Shen Jihong Zhang Mingyou Wang Xingchang Liu Bowei Xu Runzhang |
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| Affiliation: | 1. College of Science, Harbin Engineering University, Harbin, China;2. College of Automation, Harbin Engineering University, Harbin, China |
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| Abstract: | We study the Cauchy problem for a class of strongly damped multidimensional generalized Boussinesq equations utt?Δu?Δutt+Δ2u+Δ2utt?kΔut=Δf(u), where k is a positive constant. Under some assumptions and by using potential well method, we prove the existence and nonexistence of global weak solution without solution without establishing the local existence theory. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | stong damping Boussinesq equations Cauchy problem global existence nonexistence potential well method |
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