Gradient flow approach to an exponential thin film equation: global existence and latent singularity

Gao, Yuan; Liu, Jian-Guo; Lu, Xin Yang

ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 49.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

In this work, we study a fourth order exponential equation, $$ = Δe$$ derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data.

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