ON ASYMPTOTIC SOLUTIONS OF BOUNDARY-VALUE PROBLEMS DEFINED ON THIN DOMAINS.

Gerald W. Young; Stephen H. Davis

doi:10.1090/qam/766877

ON ASYMPTOTIC SOLUTIONS OF BOUNDARY-VALUE PROBLEMS DEFINED ON THIN DOMAINS.

Gerald W. Young^*, Stephen H. Davis

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

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5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	403-409
Number of pages	7
Journal	Quarterly of Applied Mathematics
Volume	42
Issue number	4
DOIs	https://doi.org/10.1090/qam/766877
State	Published - 1985

ASJC Scopus subject areas

Applied Mathematics

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title = "ON ASYMPTOTIC SOLUTIONS OF BOUNDARY-VALUE PROBLEMS DEFINED ON THIN DOMAINS.",

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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N2 - 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.

AB - 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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ON ASYMPTOTIC SOLUTIONS OF BOUNDARY-VALUE PROBLEMS DEFINED ON THIN DOMAINS.

Abstract

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