Discontinuous Solutions Of Semilinear Differential-Algebraic Equations Part 2: Rho-Consistency.

Abstract

Part 1 of this paper presented a theory of distribution solutions of semilinear differential-algebraic equations (DAE's). In particular, it was shown that uniqueness of solutions of initial value problems breaks down completely in the class of discontinuous solutions. Here a mathematical procedure is introduced for selecting physically acceptable solutions which satisfy some new consistency condition relative to admissible perturbations of the original DAE. Several nonlinear circuit examples are given to support the theory. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1994
Accession Number
ADA292285

Entities

People

  • Patrick J. Rabier
  • Werner Rheinboldt

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Advanced Electronics
  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Capacitors
  • Circuits
  • Consistency
  • Continuity
  • Differential Equations
  • Discontinuities
  • Eigenvalues
  • Electrical Circuits
  • Equations
  • Mathematics
  • Networks
  • Perturbation Theory
  • Perturbations
  • Standards
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design