Qualitative analysis of solutions for a parabolic m(x)- biharmonic equation with logarithmic nonlinearity

Abstract

In this paper, we consider a nonlinear parabolic m(x)- biharmonic equation with logarithmic source terms. Applying the potential well method combined with the Nehari manifold, the global existence and blow-up of weak solutions is proved. In addition, we establish decay estimates for the global weak solutions.