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Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik

A note on front tracking and the equivalence between viscosity solutions of Hamilton-Jacobi equations and entropy solutions of scalar conservation laws. (English) Zbl 1010.35026

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 50, No. 4, 455-469 (2002).
The paper deals with the investigation of Hamilton-Jacobi equations which are closely related to scalar conservation laws. Thereby, a proof concerned with the equivalence between the unique viscosity solution of the Hamilton-Jacobi equation and the unique entropy solution of the corresponding scalar conservation law is presented. Furthermore, a front tracking algorithm for Hamilton-Jacobi equations in one dimension is derived.
Reviewer: A.Meister (Hamburg)

Cited in 23 Documents

MSC:

35F25 Initial value problems for nonlinear first-order PDEs
35L65 Hyperbolic conservation laws

Keywords:

front tracking algorithm
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References:

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