Preprint 1997-026

Numerical Passage from Systems of Conservation Laws to Hamilton-Jacobi Equations, and a Relaxation Scheme

Abstract: In this paper we study the numerical transition from a Hamilton-Jacobi (H-J) equation to its associated system of conservation laws in arbitrary space dimensions. We first study how, in a very generic setting, one can recover the viscosity solution of the H-J equation using the numerical solution of the system of conservation laws. We then introduce a simple, second order relaxation scheme to solve the underlying weakly hyperbolic system of conservation laws.

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Title:

Numerical Passage from Systems of Conservation Laws to Hamilton-Jacobi Equations, and a Relaxation Scheme

Author(s):

Shi Jin , mailto:jin@math.gatech.edu

Zhouping Xin, mailto:xinz@cims.nyu.edu

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mailto:jin@math.gatech.edu October 7 1997.