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PHYSICAL SOLUTIONS OF THE HAMILTON-JACOBI NALINI ANANTHARAMAN, RENATO ITURRIAGA, PABLO PADILLA,
 

Summary: PHYSICAL SOLUTIONS OF THE HAMILTON-JACOBI
EQUATION
NALINI ANANTHARAMAN, RENATO ITURRIAGA, PABLO PADILLA,
AND H´ECTOR S´ANCHEZ-MORGADO
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 hy-
perbolic 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.
1. Introduction
Let L be a strictly convex and superlinear Lagrangian of class C3
on
the d-dimensional torus Td
, and let H be the associated Hamiltonian
via the Legendre transformation:
L : Td
× Rd

  

Source: Anantharaman, Nalini - Centre de Mathématiques Laurent Schwartz, École Polytechnique

 

Collections: Mathematics