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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.
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
- No. of pages:
- © Academic Press 1980
- 28th January 1980
- Academic Press
- eBook ISBN: