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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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Singular perturbations for systems of linear partial differential equations
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by A. Livne and Z. Schuss PDF
Trans. Amer. Math. Soc. 190 (1974), 335-343 Request permission

Abstract:

We consider the system of linear partial differential equations $\varepsilon {A^{ij}}u_{ij}^\varepsilon + {B^i}u_i^\varepsilon + C{u^\varepsilon } = f$ where ${A^{ij}},{B^i}$ are symmetric $m \times m$ matrices and — C is a sufficiently large positive definite matrix. We prove that under suitable conditions ${\left \| {{u^\varepsilon } - u} \right \|_{{L^2}}} \leq c\surd \varepsilon {\left \| f \right \|_{{H^1}}}$ where u is the solution of a suitable boundary value problem for the system ${B^i}{u_i} + Cu = f$.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 190 (1974), 335-343
  • MSC: Primary 35B25
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0340780-6
  • MathSciNet review: 0340780