Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients
- 1 March 2006
- journal article
- research article
- Published by Informa UK Limited in Communications in Partial Differential Equations
- Vol. 31 (3), 371-395
- https://doi.org/10.1080/03605300500358095
Abstract
In this paper, the question of existence and uniqueness for entropy solutions of scalar conservation laws with a flux function which is discontinuous with respect to the space variable is investigated. We show that no extra assumption of convexity or genuine non-linearity with respect to the state variable of the flux function is required for the problem to be well-posed and prove it. The proof uses a kinetic formulation of the conservation law.Keywords
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