Singular Perturbations and Asymptotics - 1st Edition - ISBN: 9780124932609, 9781483264578

Singular Perturbations and Asymptotics

1st Edition

Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin—Madison, May 28-30, 1980

Editors: Richard E. Meyer Seymour V. Parter
eBook ISBN: 9781483264578
Imprint: Academic Press
Published Date: 28th January 1980
Page Count: 418
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Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics.

The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications.

The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations.

The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.

Table of Contents



I. Theory of Singular Layer Problems

On Some Basic Concepts in the Analysis of Singular Perturbations

Limit Process Expansions and Approximate Equations

Some Old and New Results on Singularly Perturbed Boundary Value Problems

On Multiple Solutions of Singularly Perturbed Systems in the Conditionally Stable Case

II. Resonance in Singular Perturbations and Applications to Physical Chemistry

Singular Perturbations, Stochastic Differential Equations, and Applications

The Singularly Perturbed Turning-Point Problem: A Spectral Approach

The Singularly Perturbed Turning-Point Problem: A Geometric Approach

III. Multivariate Methods and Applications

Passage Through Resonance

A Comparison of Perturbation Methods for Nonlinear Hyperbolic Waves

Asymptotic Calculus of Variations

IV. Turning-Point Theory and Applications

Turning-Point Problems for Ordinary Differential Equations of Hydrodynamic Type

The General Connection-Formula Problem for Linear Differential Equations of the Second Order

Connection Formulas and Behavior in the Large for Solutions of Linear Differential Equations Depending Singularly on a Parameter

Connection Problems in the Parameterless Case: Progress and More Problems

Some New Results on Power-Series Solutions of Algebraic Differential Equations



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© Academic Press 1980
Academic Press
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About the Editor

Richard E. Meyer

Seymour V. Parter

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