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

 

Maximal positive boundary value problems as limits of singular perturbation problems


Authors: Claude Bardos and Jeffrey Rauch
Journal: Trans. Amer. Math. Soc. 270 (1982), 377-408
MSC: Primary 35B25; Secondary 35F05, 35L40
MathSciNet review: 645322
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Abstract: We study three types of singular perturbations of a symmetric positive system of partial differential equations on a domain $ \Omega \subset {{\mathbf{R}}^n}$. In all cases the limiting behavior is given by the solution of a maximal positive boundary value problem in the sense of Friedrichs. The perturbation is either a second order elliptic term or a term large on the complement of $ \Omega $. The first corresponds to a sort of viscosity and the second to physical systems with vastly different properties in $ \Omega $ and outside $ \Omega $. The results show that in the limit of zero viscosity or infinitely large difference the behavior is described by a maximal positive boundary value problem in $ \Omega $. The boundary condition is determined in a simple way from the system and the singular terms.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0645322-8
PII: S 0002-9947(1982)0645322-8
Keywords: Singular perturbations, boundary layers, maximal positive boundary value problems
Article copyright: © Copyright 1982 American Mathematical Society