Conservation Laws with Discontinuous Flux Functions
Open Access
- 1 March 1993
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 24 (2) , 279-289
- https://doi.org/10.1137/0524018
Abstract
The author studies the initial value problem for the scalar conservation law $u_t + f(u)_x = 0$ in one spatial dimension. The flow function may be discontinuous with a finite number of jump discontinuities. This paper proves existence of a weak solution, and the proof is constructive, suggesting a numerical method for the problem.
Keywords
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