关键词: 变指数, 对数非局部项, 伪抛物方程, 爆破

Abstract: Firstly, we used the potential well theory, the inverse Sobolev inequality, Fountain’s theorem and other tools to discuss  the blow-up problem of the solution to a class of pseudo-parabolic equations with variable exponential logarithmic nonlocal terms and singular potentials, and obtained the results of the solution of the problem to blow-up in finite time at arbitrarily high initial energy levels. Secondly, by combining  the Gagliardo-Nirenberg interpolation inequality and  Sobolev embedding method, and by constructing auxiliary functions, we gave the upper and lower bounds estimates for  the blow-up time of the solutions to the problem  under appropriate conditions.

Key words:  , variable exponent, logarithmic nonlocal term, pseudo-parabolic equation, blow-up