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Multiscale problems and homogenization for second-order Hamilton–Jacobi equations |
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| Authors: | Olivier Alvarez Martino Bardi Claudio Marchi |
| Institution: | aUMR 60-85, Université de Rouen, 76821 Mont-Saint Aignan cedex, France;bDipartimento di Matematica Pura ed Applicata, Università di Padova, via Trieste 63, 35121 Padova, Italy;cDipartimento di Matematica, Università della Calabria, Ponte Bucci 30B, 87036 Rende (CS), Italy |
| Abstract: | We prove a general convergence result for singular perturbations with an arbitrary number of scales of fully nonlinear degenerate parabolic PDEs. As a special case we cover the iterated homogenization for such equations with oscillating initial data. Explicit examples, among others, are the two-scale homogenization of quasilinear equations driven by a general hypoelliptic operator and the n-scale homogenization of uniformly parabolic fully nonlinear PDEs. |
| Keywords: | Singular perturbations Viscosity solutions Nonlinear parabolic equations Hamilton– Jacobi equations Bellman– Isaacs equations Ergodicity Stabilization Homogenization Iterated homogenization Multiscale problem Oscillating initial data Hypoelliptic operators |
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