Asymptotic analysis for a pseudo-parabolic equation with nonstandard growth conditions

Abstract

The main goal of this work is to study a semilinear pseudo-parabolic equation with nonstandard growth conditions. For initial energy , by using the generalized potential well method, we establish a sharp threshold result on global existence or blow-up weak solution. On the other hand, we also show the asymptotic behavior of solutions and the blow-up time estimates. The optimal estimations: the asymptotic behavior are obtained when the blow-up occurs. Moreover, for high initial energy , we illustrate the conditions on global existence or blow-up.