https://hal.inria.fr/hal-00664455Bardi, MartinoMartinoBardiDipartimento di Matematica Pura e Applicata [Padova] - Universita degli Studi di PadovaTerrone, GabrieleGabrieleTerroneDepartment of Mathematics [Lisbonne] - IST - Instituto Superior Técnico, Universidade Técnica de LisboaOn the Homogenization of some Non-coercive Hamilton-Jacobi-Isaacs EquationsHAL CCSD2011[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Bouzat, Estelle2012-01-30 16:07:092018-06-14 10:54:022012-01-30 20:42:58enPreprints, Working Papers, ...application/pdf1We study the homogenization of Hamilton-Jacobi equations with oscillating initial data and non-coercive Hamiltonian, mostly of the Bellman-Isaacs form arising in optimal control and differential games. We describe classes of equations for which pointwise homogenization fails for some data. We prove locally uniform homogenization for various Hamiltonians with some partial coercivity and some related restrictions on the oscillating variables, mostly motivated by the applications to differential games, in particular of pursuit-evasion type. The effective initial data are computed under some assumptions of asymptotic controllability of the underlying control system with two competing players.