Homogenization of monotone systems of Hamilton-Jacobi equations

Fabio Camilli; Olivier Ley; Paola Loreti

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 1, page 58-76
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Camilli, Fabio, Ley, Olivier, and Loreti, Paola. "Homogenization of monotone systems of Hamilton-Jacobi equations." ESAIM: Control, Optimisation and Calculus of Variations 16.1 (2010): 58-76. <http://eudml.org/doc/250720>.

@article{Camilli2010,
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. },
author = {Camilli, Fabio, Ley, Olivier, Loreti, Paola},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Systems of Hamilton-Jacobi equations; viscosity solutions; homogenization; Hamilton-Jacobi equations; monotone systems},
language = {eng},
month = {1},
number = {1},
pages = {58-76},
publisher = {EDP Sciences},
title = {Homogenization of monotone systems of Hamilton-Jacobi equations},
url = {http://eudml.org/doc/250720},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Camilli, Fabio
AU - Ley, Olivier
AU - Loreti, Paola
TI - Homogenization of monotone systems of Hamilton-Jacobi equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/1//
PB - EDP Sciences
VL - 16
IS - 1
SP - 58
EP - 76
AB - 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.
LA - eng
KW - Systems of Hamilton-Jacobi equations; viscosity solutions; homogenization; Hamilton-Jacobi equations; monotone systems
UR - http://eudml.org/doc/250720
ER -

References

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  14. H. Ishii and S. Koike, Viscosity solutions for monotone systems of second-order elliptic PDEs. Comm. Partial Differential Equations16 (1991) 1095–1128.  Zbl0742.35022
  15. P.-L. Lions and P.E. Souganidis, Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting. Comm. Pure Appl. Math.56 (2003) 1501–1524.  Zbl1050.35012
  16. P.-L. Lions, B. Papanicolaou and S.R.S. Varadhan, Homogenization of Hamilton-Jacobi equations. Preprint (1986).  
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