Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35L65

Retrieve articles in all journals with MSC: 35L65


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