Two new blow-up conditions for a pseudo-parabolic equation with logarithmic nonlinearity
Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1285-1296
Published online September 30, 2019
Hang Ding, Jun Zhou
Southwest University; Southwest University
Abstract : This paper deals with the blow-up phenomenon of solutions to a pseudo-parabolic equation with logarithmic nonlinearity, which was studied extensively in recent years. The previous result depends on the mountain-pass level $d$ (see \eqref{d} for its definition). In this paper, we obtain two blow-up conditions which do not depend on $d$. Moreover, the upper bound of the blow-up time is obtained.
Keywords : pseudo-parabolic equation, logarithmic nonlinearity, critical initial energy, blow-up
MSC numbers : 35K58, 35K15, 35B40
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