Singular Perturbations of Bifurcations,

Abstract

An asymptotic theory is presented to analyze perturbations of bifurcations of the solutions of nonlinear problems. The perturbations may result from imperfections, impurities or other inhomogeneities in the corresponding physical problem. It is shown that for a wide class of problems the perturbations are singular. The method of matched asymptotic expansions is used to obtain asymptotic expansions of the solutions. Global representations of the solutions of the perturbed problem are obtained when the bifurcation solutions are known globally. This procedure also gives a quantitative method for analyzing singularities of nonlinear mappings and their unfoldings. Applications are given to a simple elasticity problem, and to nonlinear boundary value problems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1976
Accession Number
ADA033999

Entities

People

  • Bernard J. Matkowsky
  • Edward L. Reiss

Organizations

  • New York University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Buckling
  • Coefficients
  • Composite Materials
  • Differential Equations
  • Diffusion
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Intervals
  • New York
  • Notation
  • Perturbations
  • Power Series

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Operations Research
  • Structural Dynamics.