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Homogenization of monotone systems of Hamilton-Jacobi equations

Published online by Cambridge University Press:  21 October 2008

Fabio Camilli ,
Olivier Ley  and
Paola Loreti
Fabio Camilli
Affiliation:
Dip. di Matematica Pura e Applicata, Univ. dell'Aquila, loc. Monteluco di Roio, 67040 l'Aquila, Italy. camilli@ing.univaq.it
Olivier Ley
Affiliation:
Université François-Rabelais, Tours; Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Fédération de Recherche Denis Poisson (FR 2964); Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France. ley@lmpt.univ-tours.fr
Paola Loreti
Affiliation:
Dip. di Metodi e Modelli Matematici per le Scienze Applicate, Facoltà di Ingegneria, Sapienza Università di Roma, via Scarpa 16, 00161 Roma, Italy. loreti@dmmm.uniroma1.it
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Abstract

In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the uniform convergence of the solution of the oscillating systems to the bounded uniformly continuous solution of the homogenized system.

Keywords

Systems of Hamilton-Jacobi equationsviscosity solutionshomogenization
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 1 , January 2010 , pp. 58 - 76
Copyright
© EDP Sciences, SMAI, 2008

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