Systems of Weakly Coupled Hamilton-Jacobi Equations with Implicit Obstacles

Gomes, Diogo ; Serra, António

Canadian journal of mathematics, Tome 64 (2012) no. 6, pp. 1289-1309

Résumé

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 $\text{KAM}$ 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.

Détail

DOI : 10.4153/CJM-2011-085-7

Mots-clés : 35F60, 35F21, 35D40, Hamilton–Jacobi equations, switching costs, viscosity solutions

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