A STABILITY THEORY FOR NONLINEAR MIXED INITIAL BOUNDARY VALUE PROBLEMS,

Abstract

This paper discusses the notion of complete stability of mixed initial boundary problems for systems of partial differential equations. The discussion is not restricted to the purely linear case. Moreover, the boundary conditions are permitted to take the form of systems of nonlinear ordinary differential equations. The principal result of the paper is a method for constructing so-called Liapounov functionals by means of which the stability statement is obtained. A second result is a theorem which shows that complete stability follows from the existence of a Liapounov functional. A number of examples are included.

Document Details

Document Type
Technical Report
Publication Date
Jun 19, 1964
Accession Number
AD0618851

Entities

People

  • R. K. Brayton
  • W. L. Miranker

Organizations

  • IBM Thomas J. Watson Research Center

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Structural Dynamics.