Homogenization of First-Order Equations with (u/ε) -Periodic Hamiltonians. Part I: Local Equations

Imbert, Cyril; Monneau, Régis

Imbert, Cyril; Monneau, Régis (2008), Homogenization of First-Order Equations with (u/ε) -Periodic Hamiltonians. Part I: Local Equations, Archive for Rational Mechanics and Analysis, 187, 1, p. 49-89. http://dx.doi.org/10.1007/s00205-007-0074-4

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00016270

Date

2008

Journal name

Archive for Rational Mechanics and Analysis

Volume

187

Number

Publisher

Springer

Pages

49-89

Abstract (EN)

In this paper, we present a result of homogenization of first-order Hamilton–Jacobi equations with ( u/ε )-periodic Hamiltonians. On the one hand, under a coercivity assumption on the Hamiltonian (and some natural regularity assumptions), we prove an ergodicity property of this equation and the existence of nonperiodic approximate correctors. On the other hand, the proof of the convergence of the solution, usually based on the introduction of a perturbed test function in the spirit of Evans’s work, uses here a twisted perturbed test function for a higher-dimensional problem.

Subjects / Keywords

periodic homogenization; Hamilton-Jacobi equations; correctors; perturbed test function; coercivity