Neumann Type Boundary Conditions for Hamilton-Jacobi Equations.

Abstract

In this paper, we present a notion of viscosity solutions of Hamilton-Jacobi equations for Neumann type boundary conditions (or more generally oblique derivative). In particular we prove the existence, uniqueness, stability of such solutions and we show that the vanishing viscosity method yields such solutions. Next, we check that value functions of control problems or differential games problems for reflected dynamical processes are solutions in that sense of the associated Bellman or Isaacs equations. Finally, we consider the ergodic problems.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1984
Accession Number
ADA149069

Entities

People

  • P. L. Lyons

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Analogs
  • Boundaries
  • Cauchy Problem
  • Classification
  • Computer Programming
  • Continuity
  • Differential Equations
  • Diffusion
  • Dynamic Programming
  • Equations
  • Inequalities
  • Mathematics
  • Partial Differential Equations
  • Reflection
  • Scalar Functions
  • Sequences
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.