Global well-posedness for strongly damped multidimensional generalized Boussinesq equations

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• 作者：Shen Jihong ; Zhang Mingyou ; Wang Xingchang ; Liu Bowei and Xu Runzhang
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：39
• 期：15
• 页码：4437-4450
• 全文大小：254K
• ISSN：1099-1476

文摘

We study the Cauchy problem for a class of strongly damped multidimensional generalized Boussinesq equations u_tt−Δu−Δu_tt+Δ²u+Δ²u_tt−kΔu_t=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