Homogenization of First-Order Equations with (u/ε) -Periodic Hamiltonians. Part I: Local Equations
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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00016270
Journal nameArchive for Rational Mechanics and Analysis
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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 / Keywordsperiodic homogenization; Hamilton-Jacobi equations; correctors; perturbed test function; coercivity
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Homogenization of First-Order Equations with (u/ε) -Periodic Hamiltonians. Part II: application to dislocations dynamics Imbert, Cyril; Monneau, Régis; Rouy, Elisabeth (2007) Document de travail / Working paper