Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On asymptotic solutions of boundary value problems defined on thin domains

Authors: Gerald W. Young and Stephen H. Davis
Journal: Quart. Appl. Math. 42 (1985), 403-409
MSC: Primary 35B40; Secondary 35J05, 76D10
DOI: https://doi.org/10.1090/qam/766877
MathSciNet review: 766877
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Abstract: The solution of the Poisson equation subject to Dirichlet conditions is examined asymptotically on thin domains. The evolution of the structure of the solution is followed as the shape of the domain changes. It is found that the ``end wall'' boundary layers present when the domain is rectangular, shrink and weaken as the endwalls become less sloped and vanish when the domain slope is uniformly bounded. Such structural changes are important in certain viscous flows containing moving contact lines.

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DOI: https://doi.org/10.1090/qam/766877
Article copyright: © Copyright 1985 American Mathematical Society

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