Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The Riemann problem for nonconvex scalar conservation laws and Hamilton-Jacobi equations
HTML articles powered by AMS MathViewer

by Stanley Osher PDF
Proc. Amer. Math. Soc. 89 (1983), 641-646 Request permission

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35L65
  • Retrieve articles in all journals with MSC: 35L65
Additional Information
  • © Copyright 1983 American Mathematical Society
  • 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