Discontinuous Solutions Of Semilinear Differential-Algebraic Equations Part I: Distribution Solutions.

Abstract

There is strong physical evidence that a full treatment of differential-algebraic equations should be incorporate solutions with jump discontinuities. It is shown here that for semilinear problems the setting of distributions allows for the development of a theory where indeed such discontinuities may occur. This approach also settles the problem of inconsistent initial conditions in a very simple way. On the other hand, new issues arise as not only uniqueness. but even countability of the number of solutions of initial value problems may now be lost. A physically motivated but purely mathematical selection procedure to overcome this difficulty is discussed in part 2 of this paper. (AN)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1994
Accession Number
ADA292286

Entities

People

  • Patrick J. Rabier
  • Werner Rheinboldt

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Abstracts
  • Autonomous Systems
  • Consistency
  • Differential Equations
  • Discontinuities
  • Electrical Networks
  • Equations
  • Information Operations
  • Intervals
  • Linear Algebra
  • Mathematics
  • Network Science
  • New York
  • Notation
  • Perturbation Theory
  • Perturbations
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Educational Psychology
  • Fluid Dynamics.