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Introduction to the General Theory of Singular Perturbations
S. A. Lomov
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Translations of Mathematical Monographs
1992; 375 pp; hardcover
Volume: 112
ISBN-10: 0-8218-4569-1
ISBN-13: 978-0-8218-4569-1
List Price: US$135
Member Price: US$108
Order Code: MMONO/112
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This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects, and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.

Readership

Researchers and students in physics, mathematics and engineering.

Table of Contents

  • Introduction. General survey
Part I.Asymptotic integration of various problems for ordinary differential equations:
  • The method of regularization of singular perturbations
  • Asymptotic integration of a boundary value problem
  • Asymptotic integration of linear integro-differential equations;
  • Some problems with rapidly oscillating coefficients
  • Problems with an unstable spectrum
  • Singularly perturbed problems for nonlinear equations
Part II.Singularly perturbed partial differential equations:
  • Asymptotic integration of linear parabolic equations
  • Application of the regularization method to some elliptic problems in a cylindrical domain
  • Asymptotic integration of some singularly perturbed evolution equations
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