Analysis finds global existence and blow-up of weak solutions in a fourth-order parabolic equation, indicating new methods improve understanding of energy classification.
This paper deals with a fourth‐order parabolic equation modeling epitaxial thin film growth, subject to the Navier boundary conditions. By the variational methods and embedding inequalities, we determine the complete classification of global existence and blow‐up of weak solutions by covering all kinds of initial energy characterized with the mountain pass level . The present results of this paper complement and improve a recent paper in Appl. Math. Lett . 111 (2021) 106609.
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Xizheng Sun (2025) studied this question.
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