Singular solutions for the fourth‐order parabolic equation with nonstandard growth conditions and absorption

Abstract

This paper deals with the fourth‐order parabolic equation in a bounded domain, subject to homogeneous Navier boundary conditions. Under some conditions on the variable exponents, we give a complete and optimal classification on the singularity of solutions, characterized by the signs of the Nehari energy and the difference between the initial energy and the potential depth.