Homogenization of First-Order Equations with $$(u/\varepsilon)$$ -Periodic Hamiltonians. Part I: Local Equations | Zendy

Cyril Imbert | Zendy; Régis Monneau | Zendy

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

Author(s) -

Cyril Imbert,

Régis Monneau

Publication year - 2007

Publication title -

archive for rational mechanics and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.933

H-Index - 106

eISSN - 1432-0673

pISSN - 0003-9527

DOI - 10.1007/s00205-007-0074-4

Subject(s) - homogenization (climate) , mathematics , ergodicity , hamilton–jacobi equation , hamiltonian (control theory) , mathematical analysis , hamiltonian system , mathematical physics , pure mathematics , biodiversity , ecology , mathematical optimization , statistics , biology

30 pagesInternational audienceIn this paper, we present a result of homogenization of first order Hamilton-Jacobi equations with ($u/\varepsilon$)-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 non periodic 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' work, uses here a twisted perturbed test function for a higher dimensional problem

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