Precise decay rates of global solutions and an explicit upper bound of the blow‐up time to a pseudo‐parabolic equation

Abstract

This paper deals with a pseudo‐parabolic equation with nonstandard growth conditions. Some results on global existence, blow‐up, and asymptotic behavior of weak solutions were obtained. The purpose of this paper is to give results to some unsolved questions. First, the precise decay rates for global solutions are derived. Second, an explicit upper bound of the blow‐up time is obtained when the initial energy is low.