Two Approximations of Solutions of Hamilton-Jacobi Equations.

Abstract

Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations, control theory and differential games. The associated initial-value problems almost never have global-time classical solutions, and one must deal with suitable generalized solutions. The correct class of generalized solutions has only recently been established by the authors. This article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates. Analogous results are proved by similar means for the method of vanishing viscosity. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1982
Accession Number
ADA124359

Entities

People

  • Michael G. Crandall
  • Pierre Louis Lions

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Complex Variables
  • Computational Fluid Dynamics
  • Computational Science
  • Continuity
  • Differential Equations
  • Equations
  • Fluid Mechanics
  • Functions (Mathematics)
  • Inequalities
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
  • Standards
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis