Energy classification in a nonstandard fourth‐order parabolic equation with a Navier boundary condition

Abstract

This paper deals with a fourth-order parabolic equation involving variable exponents, subject to Navier boundary conditions. We firstly give an optimal classification on the initial energy for blow-up or global solutions, which is characterized by the sign of the Nehari energy and the difference between the initial energy and the depth of the potential well. Then, large time estimates of solutions are obtained. The results of the paper extend and complete the ones in "Applied Mathematics Letters 78(2018)141-146." KEYWORDS asymptotic behavior, blow-up, extinction, higher order parabolic equation, potential well method MSC CLASSIFICATION