Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The two-variable technique for singular partial differential problems and its justification

Author: M. Bouthier
Journal: Quart. Appl. Math. 38 (1980), 263-276
MSC: Primary 35B25
DOI: https://doi.org/10.1090/qam/592195
MathSciNet review: 592195
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Abstract: Dirichlet problems with a small parameter in factor of the highest derivative are considered for bounded domains. A two-variable technique is formalized in order to carry out the study of the main boundary layer. A ``secular `` hypothesis is made, and a unique and uniformly valid asymptotic expansion is obtained. However, it is shown that the ``secular'' hypothesis may be weakened and this yields a whole set of expansions. Then the asymptotic validity of each expansion in the set can be proven for second-order operators by means of an extension of a theorem due to Eckhaus and Jager.

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DOI: https://doi.org/10.1090/qam/592195
Article copyright: © Copyright 1980 American Mathematical Society

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