On numerical approximation  of the Hamilton-Jacobi-transport system arising in high frequency approximations

Yves Achdou; Fabio Camilli; Lucilla Corrias

doi:10.3934/dcdsb.2014.19.629

Article Contents

2014, Volume 19, Issue 3: 629-650. Doi: 10.3934/dcdsb.2014.19.629

This issue Previous Article Next Article Regularity of the attractor for a Bose-Einstein equation in a two dimensional unbounded domain

On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations

1.
Université Paris Diderot, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS, Sorbonne Paris Cité F-75205 Paris
2.
"Sapienza" Università di Roma, Dip. di Scienze di Base e Applicate per l'Ingegneria, via Scarpa 16, 0161 Roma
3.
Laboratoire d'Analyse et Probabilité, Université d'Evry Val d'Essonne, 23 Bd. de France, F-91037 Evry Cedex

Received: December 31, 2012

Revised: September 30, 2013

Published: April 2014

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Abstract

In the present article, we study the numerical approximation of a system of Hamilton-Jacobi and transport equations arising in geometrical optics. We consider a semi-Lagrangian scheme. We prove the well posedness of the discrete problem and the convergence of the approximated solution toward the viscosity-measure valued solution of the exact problem.

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Mathematics Subject Classification: Primary: 65M12; Secondary: 35F25, 35R05, 49L25.

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