Asymptotic analysis for a pseudo-parabolic equation with nonstandard growth conditions. Issue 13 (2nd September 2022) - Qu, Chengyuan; Zhou, Wenshu
Abstract : The main goal of this work is to study a semilinear pseudo-parabolic equation with nonstandard growth conditions. For initial energy J ( u 0 ) ≤ d, 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 J ( u 0 ) > d, we illustrate the conditions on global existence or blow-up.