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

摘要

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 (C) 2015 John Wiley & Sons, Ltd.