Asymptotic behavior of α-entropy solutions to the thin film equation on the sphere

Journal of Mathematical Analysis and Applications 2026 Open access

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Authors: Roman M. Taranets, Marina Chugunova, Hangjie Ji
DOI: 10.1016/j.jmaa.2026.130491
Cited by: 1
References: 28

Abstract

We investigate the existence and behavior of α -entropy solutions to the double-degenerate thin-film equation, which models viscous coating flows on spherical surfaces. Our results show that these solutions exhibit both finite-speed propagation and a waiting-time phenomenon. Furthermore, we derive an upper bound for the interface propagation rate and a lower bound for the waiting time. Numerical simulations are also presented to support the analytical results.

Fields of Study & Subjects

Fluid Dynamics and Thin Films Navier-Stokes equation solutions Solidification and crystal growth phenomena

Publication details

Journal / source
Journal of Mathematical Analysis and Applications
Publisher
Elsevier BV
Volume
560
Issue
1
Pages
130491–130491
Publication date
5 February 2026
Language
EN