Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations

2016 ◽  
Vol 55 (4) ◽  
Author(s):  
Alessio Figalli ◽  
Diogo Gomes ◽  
Diego Marcon
Keyword(s):  
Kam Theory ◽  
Coupled System ◽  
Weak Kam Theory ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Jacobi Equations

Systems of Weakly Coupled Hamilton-Jacobi Equations with Implicit Obstacles

2012 ◽  
Vol 64 (6) ◽  
pp. 1289-1309 ◽  
Author(s):  
Diogo Gomes ◽  
António Serra
Keyword(s):  
Dirichlet Problem ◽  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Kam Theory ◽  
Optimal Switching ◽  
Uniqueness Of Solutions ◽  
Weak Kam Theory ◽  
Weakly Coupled ◽  
Aubry Set ◽  
Jacobi Equations

Abstract In this paper we study systems of weakly coupled Hamilton-Jacobi equations with implicit obstacles that arise in optimal switching problems. Inspired by methods from the theory of viscosity solutions and weak KAM theory, we extend the notion of Aubry set for these systems. This enables us to prove a new result on existence and uniqueness of solutions for the Dirichlet problem, answering a question of F. Camilli, P. Loreti, and N. Yamada.

scholarly journals Convergence of the solutions of discounted Hamilton–Jacobi systems

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrea Davini ◽  
Maxime Zavidovique
Keyword(s):  
Riemannian Manifold ◽  
Coupled System ◽  
Discount Factor ◽  
Limit System ◽  
Specific Solution ◽  
Closed Riemannian Manifold ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Jacobi Equations ◽  
Minimizing Measures

Abstract We consider a weakly coupled system of discounted Hamilton–Jacobi equations set on a closed Riemannian manifold. We prove that the corresponding solutions converge to a specific solution of the limit system as the discount factor goes to 0. The analysis is based on a generalization of the theory of Mather minimizing measures for Hamilton–Jacobi systems and on suitable random representation formulae for the discounted solutions.

Distribution of the Fission Reaction rate in a Weakly Coupled System for Testing the Checkerboard Model

Atomic Energy ◽  
2014 ◽  
Vol 116 (6) ◽  
pp. 421-427 ◽  
Author(s):  
E. F. Mitenkova ◽  
D. A. Koltashev ◽  
P. A. Kizub
Keyword(s):  
Reaction Rate ◽  
Coupled System ◽  
Fission Reaction ◽  
Weakly Coupled ◽  
Weakly Coupled System
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