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Introduction to the General Theory of Singular Perturbations
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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.Table of contents: Introduction; General survey; Part I: Asymptotic integration ...
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.
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 co-efficients; Problems with an unstable spectrum; Singularly perturbed problems for nonlinear equations; Part II: Singularly perturbed partial differential equations: Asymptotic integration of linear parabolic equations; Applications of the regularization method to some elliptic problems in a cylindrical domain; Asymptotic integration of some singularly perturbed evolution equations.
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 co-efficients; Problems with an unstable spectrum; Singularly perturbed problems for nonlinear equations; Part II: Singularly perturbed partial differential equations: Asymptotic integration of linear parabolic equations; Applications of the regularization method to some elliptic problems in a cylindrical domain; Asymptotic integration of some singularly perturbed evolution equations.