A Singular Singularly-Perturbed Linear Boundary Value Problem.

Abstract

The asymptotic solution of boundary value problems are considered for the vector system dx/dt = A(t, epsilon)x + B(t, epsilon)y + C(t, epsilon, epsilon dy/dt = E(t, epsilon)x + F(t, epsilon)y + G(t, epsilon) as epsilon approaches 0 under the assumption that the matrix F(t,0) is singular. A full set of asymptotic solutions is constructed assuming that F(t,0) can be block-diagonalized, the reduced problem is consistent, and a new stability condition holds. Boundary value problems are then solvable if an appropriate 'boundary' matrix is nonsingular for epsilon not = 0. Such problems arise in optimal control theory, among other applications.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1977
Accession Number
ADA041210

Entities

People

  • R. E. O'malley Jr.

Organizations

  • University of Arizona

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Asymptotic Series
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Control Theory
  • Differential Equations
  • Eigenvalues
  • Equations
  • Formulas (Mathematics)
  • Integral Equations
  • Layers
  • Linear Differential Equations
  • Linear Systems
  • Mathematics
  • New York
  • Nonlinear Analysis

Fields of Study

  • Mathematics

Readers

  • Linear Algebra