ON NUMERICAL APPROXIMATION OF THE HAMILTON-JACOBI-TRANSPORT SYSTEM ARISING IN HIGH FREQUENCY APPROXIMATIONS

被引：5

作者：

Achdou, Yves ^{[1
]}

Camilli, Fabio ^{[2
]}

Corrias, Lucilla ^{[3
]}

机构：

[1] Univ Paris Diderot, Lab Jacques Louis Lions, UMR 7598, UPMC,CNRS,Sorbonne Paris Cite, F-75205 Paris, France

[2] Univ Roma La Sapienza, Dip Sci Base & Applicate Ingn, I-0161 Rome, Italy

[3] Univ Evry Val dEssonne, Lab Anal & Probabilite, F-91037 Evry, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2014年 / 19卷 / 03期

关键词：

Hamilton-Jacobi equation; transport equation; viscosity solutions; measure solutions; semiconcavity; numerical approximations; OSL condition; VISCOSITY SOLUTIONS; EQUATIONS; SCHEMES; TRANSFORM;

D O I：

10.3934/dcdsb.2014.19.629

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：629 / 650

页数：22

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