Global solution and blow-up for a class of Δγ-biharmonic parabolic equations with logarithmic nonlinearity

Abstract

In this paper, we study a class of [Formula: see text]-biharmonic parabolic equations with logarithmic nonlinearity. Using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin approximation technique and the Sobolev inequality, we obtain the existence of the unique global weak solutions. In addition, we also provide sufficient conditions for the large time decay of global weak solutions and the finite time blow-up of weak solutions.