This paper deals with the fourth-order parabolic equation u t + Δ 2 u = 𝜇u p(x) − 𝜆u q(x) 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.
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