A sufficient condition for blowup of solutions to a class of pseudo-parabolic equations with a nonlocal term

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• 作者：Xiaoli Zhu ; Fuyi Li ; Zhanping Liang and Ting Rong
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：39
• 期：13
• 页码：3591-3606
• 全文大小：308K
• ISSN：1099-1476

文摘

A sufficient condition for blowup of solutions to a class of pseudo-parabolic equations with a nonlocal term is established in this paper. In virtue of the potential wells method, we first extend the results obtained by Xu and Su in [J. Funct. Anal., 264 (12): 2732-2763, 2013] to the nonlocal case and describe successfully the behavior of solutions by using the energy functional, Nehari functional, and the ground state energy of the stationary equation. Sequently, we study the boundedness and convergency of any global solution. Finally, we achieve a criterion to guarantee the blowup of solutions without any limit of the initial energy.Copyright