Blow-up and exponential decay of solutions to a class of pseudo-parabolic equation

Abstract

In this paper, we consider a class of pseudo-parabolic equation, which was studied extensively in recent years, and the main results on blow-up depend on the initial energy $J(u_0)$ (see (1.5)) and the mountain-pass level $d$ (see (1.7)). By using eigenfunction, we give a new blow-up result which does not depend on $J(u_0)$ and $d$. Moreover, we obtain the energy functional $J(u)$ (see (1.5)) decays exponentially. These results extend the previous studies on this equation.