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Stochastic homogenization of non-local Hamilton-Jacobi equations

Hajej, Ahmed (2016), Stochastic homogenization of non-local Hamilton-Jacobi equations. https://basepub.dauphine.fr/handle/123456789/17248

Type
Document de travail / Working paper
Date
2016
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Metadata
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Author(s)
Hajej, Ahmed
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We study the homogenization of non-local Hamilton-Jacobi equations in stationary ergodic settings. These equations can be seen as a level-set approach of front propagation problems that move in the normal direction with non-local velocities. We first identify the effective Hamiltonian and an approximate corrector by studying the associated metric problem. Then, we prove the main homogenization result by means of a non-local version of the perturbed test function method.
Subjects / Keywords
non-local Hamilton-Jacobi equations; front propagation problems; level-set approach; homogenization in random media; metric problems; perturbed test function method; viscosity solution.