Blow-up phenomena for a pseudo-parabolic equation with p-Laplacian and logarithmic nonlinearity terms

摘要

This paper deals with a pseudo-parabolic equation with p-Laplacian and logarithmic nonlinearity terms under homogeneous Dirichlet boundary condition in a smooth bounded domain, which was studied in [12], and the global existence and finite time blow up of the weak solution were studied under different energy levels. We generalize and extend those results by discussing the asymptotic behavior of the weak solution and proving that the weak solution converges to the corresponding stationary solution as time tends to infinity. Moreover, a lower and an upper bound estimation for blow-up time and rate are obtained for the blow-up weak solution in different initial energy cases. Furthermore, we establish the weak solution with high initial energy that is global bounded or blow-up under some sufficient conditions as well as a nonblow-up criterion and algebraic decay result in other assumptions. (C) 2019 Elsevier Inc. All rights reserved.