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The Riemann problem for nonconvex scalar conservation laws and Hamilton-Jacobi equations


Author: Stanley Osher
Journal: Proc. Amer. Math. Soc. 89 (1983), 641-646
MSC: Primary 35L65
DOI: https://doi.org/10.1090/S0002-9939-1983-0718989-X
MathSciNet review: 718989
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Abstract: We present a closed form expression for the viscosity solution to the Riemann problem for any scalar nonconvex conservation law. We then define an analogous problem for any scalar nonconvex Hamilton-Jacobi equation and obtain its (even simpler) solution. Extensions to two (and by inference, higher) space dimensional problems, when the initial discontinuity lies on a hyperplane, are also given.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0718989-X
Keywords: Conservation law, Hamilton-Jacobi equations, Riemann problem
Article copyright: © Copyright 1983 American Mathematical Society

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