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

作者：Fengjie Li, Anqi Sun, Bingchen Liu · 发表于：Mathematical Methods in the Applied Sciences · 年份：2023 · DOI：10.1002/mma.9044 · 被引用次数：6 · 研究领域：Nonlinear Partial Differential Equations、Advanced Mathematical Modeling in Engineering、Differential Equations and Boundary Problems

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.