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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
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.

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