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Qualitative Behaviour of Solutions in Two Models of Thin Liquid Films
Joint Authors
Michal, Matthew
Chugunova, Marina
Taranets, Roman
Source
International Journal of Differential Equations
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-05-05
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
For the thin-film model of a viscous flow which originates from lubrication approximation and has a full nonlinear curvature term, we prove existence of nonnegative weak solutions.
Depending on initial data, we show algebraic or exponential dissipation of an energy functional which implies dissipation of the solution arc length that is a well known property for a Hele-Shaw flow.
For the classical thin-film model with linearized curvature term, under some restrictions on parameter and gradient values, we also prove analytically the arc length dissipation property for positive solutions.
We compare the numerical solutions for both models, with nonlinear and with linearized curvature terms.
In regimes when solutions develop finite time singularities, we explain the difference in qualitative behaviour of solutions.
American Psychological Association (APA)
Michal, Matthew& Chugunova, Marina& Taranets, Roman. 2016. Qualitative Behaviour of Solutions in Two Models of Thin Liquid Films. International Journal of Differential Equations،Vol. 2016, no. 2016, pp.1-11.
https://search.emarefa.net/detail/BIM-1105696
Modern Language Association (MLA)
Michal, Matthew…[et al.]. Qualitative Behaviour of Solutions in Two Models of Thin Liquid Films. International Journal of Differential Equations No. 2016 (2016), pp.1-11.
https://search.emarefa.net/detail/BIM-1105696
American Medical Association (AMA)
Michal, Matthew& Chugunova, Marina& Taranets, Roman. Qualitative Behaviour of Solutions in Two Models of Thin Liquid Films. International Journal of Differential Equations. 2016. Vol. 2016, no. 2016, pp.1-11.
https://search.emarefa.net/detail/BIM-1105696
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1105696