## 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.## References

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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