Weak KAM theorem for Hamilton-Jacobi equations
Dynamical Systems
2013-12-06 v1 Analysis of PDEs
Optimization and Control
Abstract
In this paper, we generalize weak KAM theorem from positive Lagrangian systems to "proper" Hamilton-Jacobi equations. We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the properties of the solution semigroup, we prove the convergence of solution semigroup and existence of weak KAM solutions for stationary equations: \begin{equation*} H(x, u, d_x u)=0. \end{equation*}
Cite
@article{arxiv.1312.1606,
title = {Weak KAM theorem for Hamilton-Jacobi equations},
author = {Xifeng Su and Jun Yan},
journal= {arXiv preprint arXiv:1312.1606},
year = {2013}
}
Comments
31 pages