Physical solutions of the Hamilton-Jacobi equation

Nalini Anantharaman; Renato Iturriaga; Pablo Padilla; Héctor Sánchez-Morgado

doi:10.3934/dcdsb.2005.5.513

Article Contents

2005, Volume 5, Issue 3: 513-528. Doi: 10.3934/dcdsb.2005.5.513

This issue Previous Article Next Article Universality of dishonesty of substochastic semigroups: Shattering fragmentation and explosive birth-and-death processes

Physical solutions of the Hamilton-Jacobi equation

1.
École Normale Supérieure, U.M.P.A., 46, allée d'Italie, 69364 Lyon Cedex 07
2.
CIMAT, A.P. 402, 3600, Guanajuato. Gto
3.
IIMAS, UNAM, Cd. Universitaria, México, D.F. 04510
4.
I. de Matemáticas, UNAM, Cd. Universitaria, México, D.F. 04510

Received: January 2004

Revised: August 2004

Published: August 2005

Abstract Related Papers Cited by

Abstract

We consider a Lagrangian system on the d-dimensional torus, and the associated Hamilton-Jacobi equation. Assuming that the Aubry set of the system consists in a finite number of hyperbolic periodic orbits of the Euler-Lagrange flow, we study the vanishing-viscosity limit, from the viscous equation to the inviscid problem. Under suitable assumptions, we show that solutions of the viscous Hamilton-Jacobi equation converge to a unique solution of the inviscid problem.

Keywords:

Mathematics Subject Classification: 37J50, 49L25, 70H20.

Citation:

Article Metrics

HTML views() PDF downloads(306) Cited by(0)

Physical solutions of the Hamilton-Jacobi equation

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Physical solutions of the Hamilton-Jacobi equation

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content