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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Liquid drops sliding down an inclined plane


Authors: Inwon Kim and Antoine Mellet
Journal: Trans. Amer. Math. Soc. 366 (2014), 6119-6150
MSC (2010): Primary 35H30, 35R35, 35Q35
Published electronically: May 22, 2014
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Abstract: We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long-time behavior for both homogeneous and inhomogeneous media (i.e. constant and non-constant contact angle). We also obtain some homogenization results.


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Additional Information

Inwon Kim
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095
Email: ikim@math.ucla.edu

Antoine Mellet
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: mellet@math.umd.edu.

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06236-3
PII: S 0002-9947(2014)06236-3
Received by editor(s): March 18, 2012
Received by editor(s) in revised form: April 10, 2013
Published electronically: May 22, 2014
Additional Notes: The first author was partially supported by NSF Grant DMS-0970072.
The second author was partially supported by NSF Grants DMS-0901340 and DMS-1201426
Article copyright: © Copyright 2014 American Mathematical Society