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.
Convergence of the solutions of discounted Hamilton-Jacobi systems / Davini, A.; Zavidovique, M.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 0:0(2021). [10.1515/acv-2018-0037]
Convergence of the solutions of discounted Hamilton-Jacobi systems
Davini A.
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2021
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.| File | Dimensione | Formato | |
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