Systems of weakly coupled Hamilton-Jacobi equations with implicit obstacles

Diogo Gomes; António Serra

doi:10.4153/CJM-2011-085-7

Systems of weakly coupled Hamilton-Jacobi equations with implicit obstacles

Diogo Gomes, António Serra

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1289-1309
Number of pages	21
Journal	Canadian Journal of Mathematics
Volume	64
Issue number	6
DOIs	https://doi.org/10.4153/CJM-2011-085-7
State	Published - Dec 2012
Externally published	Yes

Keywords

Hamilton-Jacobi equations
Switching costs
Viscosity solutions

ASJC Scopus subject areas

General Mathematics

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10.4153/CJM-2011-085-7

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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.",

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AB - 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.

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KW - Viscosity solutions

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Systems of weakly coupled Hamilton-Jacobi equations with implicit obstacles

Abstract

Keywords

ASJC Scopus subject areas

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