Explicit formula for weighted scalar nonlinear hyperbolic conservation laws

Authors:
Philippe LeFloch and Jean-Claude Nédélec

Journal:
Trans. Amer. Math. Soc. **308** (1988), 667-683

MSC:
Primary 35L65

DOI:
https://doi.org/10.1090/S0002-9947-1988-0951622-X

MathSciNet review:
951622

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Abstract: We prove a uniqueness and existence theorem for the entropy weak solution of nonlinear hyperbolic conservation laws of the form

We give an explicit formula, which generalizes a result of P. D. Lax. In particular, a free boundary problem for the flux at the boundary is solved by introducing a variational inequality. The uniqueness result is obtained by extending a semigroup property due to B. L. Keyfitz.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1988-0951622-X

Article copyright:
© Copyright 1988
American Mathematical Society