Work

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

Year: 2026

Type: article

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.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2026.130491

Authors: Roman Taranets, Marina Chugunova, Hangjie Ji

Institutions: Claremont Graduate University, North Carolina State University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190