Stationary Points and Finite-Difference Schemes for Differential Inclusions.

Abstract

So called 'differential inclusions', in which the rate of change x(dot) of the state variable x is restricted to lie in a specified set F(x) (and not given exactly) arise naturally in economics, control theory and other fields. As with differential equations, one is interested in the existence of stationary points. Here it is shown that if F is tangent to a compact convex set (in a sense made precise), then the differential inclusion has a stationary point within this set. Moreover, a discrete implicit difference scheme which approximates the inclusion will also be solvable when the tangency condition holds and the initial data is chosen from the set.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1980
Accession Number
ADA086381

Entities

People

  • Jean-pierre Aubin

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algebra
  • Classification
  • Convex Sets
  • Differential Equations
  • Equations
  • Feedback
  • Inequalities
  • Lyapunov Functions
  • Mathematics
  • North Carolina
  • Numbers
  • Point Theorem
  • Real Numbers
  • Sequences
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)