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Proceedings of the American Mathematical Society

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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
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?)

  • [1] M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. MR 690039 (85g:35029)
  • [2] S. N. Kružkov, First order quasi-linear equations in several independent variables, Math. USSR Sb. 10 (1970), 217-243.
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Keywords: Conservation law, Hamilton-Jacobi equations, Riemann problem
Article copyright: © Copyright 1983 American Mathematical Society

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