Article ID Journal Published Year Pages File Type
4609342 Journal of Differential Equations 2016 38 Pages PDF
Abstract

We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter ε. We study the asymptotics, as ε goes to 0, of the corresponding value functions, and show convergence, in the sense of weak semilimits, to sub and supersolution of a suitable limit equation containing the effective Hamiltonian.The novelty of our contribution is that no compactness condition is assumed on the fast variable. This generalization requires, in order to perform the asymptotic procedure, an accurate qualitative analysis of some auxiliary equations posed on the space of fast variable. The task is accomplished using some tools of Weak KAM theory, and in particular the notion of Aubry set.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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