An Invariant Measure for the Equation u sub tt - u sub xx + u3 = 0.

Abstract

Numerical studies of the initial boundary-value problem for a semilinear wave equation subject to certain periodic boundary conditions and initial conditions suggest that solutions ultimately return to a neighborhood of the initial state after undergoing a possibly chaotic evolution. This paper considers an appropriate abstract space. In this space a finite measure is constructed. This measure is invariant under the flow generated by the hamiltonian system which corresponds to the original equation. This enables one to verify the above returning property.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1984
Accession Number
ADA147300

Entities

People

  • L. Friedlander

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Classification
  • Contracts
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Equations
  • Mathematics
  • Numbers
  • Partial Differential Equations
  • Real Numbers
  • United States
  • Wave Equations
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space