Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

Singular perturbations for systems of linear partial differential equations


Authors: A. Livne and Z. Schuss
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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\Vert {{u^\varepsilon } - u} \right\Vert _{{L^2}}} \leq c\surd \varepsilon {\left\Vert f \right\Vert _{{H^1}}}$ where u is the solution of a suitable boundary value problem for the system $ {B^i}{u_i} + Cu = f$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35B25

Retrieve articles in all journals with MSC: 35B25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0340780-6
Keywords: First order system, singular perturbations, rate of convergence
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society