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

Gerald W. Young*, Stephen H. Davis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 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 languageEnglish (US)
Pages (from-to)403-409
Number of pages7
JournalQuarterly of Applied Mathematics
Volume42
Issue number4
DOIs
StatePublished - 1985

ASJC Scopus subject areas

  • Applied Mathematics

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