Asymptotic Behavior of Gradient-Like Systems.

Abstract

For a class of gradient evolutionary equations, we prove that the w-limit set of a bounded orbit is an equilibrium point if the dimension of the null space of the linear variational operator is no more than one. This implies the result of Matano concerning a parabolic equation in one space dimension with separated boundary conditions. The statement about gradient systems is a consequence of a more general property which has applications, for example, to the stability of traveling waves. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 02, 1981
Accession Number
ADA100203

Entities

People

  • Jack K. Hale
  • Paul Massatt

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Arrhenius Equation
  • Boundaries
  • Cooperation
  • Equations
  • Formulas (Mathematics)
  • Mathematics
  • Oklahoma
  • Traveling Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Plasma Physics / Magnetohydrodynamics

Technology Areas

  • Space