Homogenization of some periodic Hamilton-Jacobi equations with defects

2022/11/29 by Yves Achdou, Achdou, Yves, Claude Le Bris +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.2211.16157

Abstract

We study homogenization for a class of stationnary Hamilton-Jacobi equations in which the Hamiltonian is obtained by perturbing near the origin an otherwise periodic Hamiltonian. We prove that the limiting problem consists of a Hamilton-Jacobi equation outside the origin, with the same effective Hamiltonian as in periodic homogenization, supplemented at the origin with an effective Dirichlet condition that keeps track of the perturbation. Various comments and extensions are discussed.

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