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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Maximal positive boundary value problems as limits of singular perturbation problems
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by Claude Bardos and Jeffrey Rauch PDF
Trans. Amer. Math. Soc. 270 (1982), 377-408 Request permission

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
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 270 (1982), 377-408
  • MSC: Primary 35B25; Secondary 35F05, 35L40
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0645322-8
  • MathSciNet review: 645322