A solution formula for a non-convex scalar hyperbolic conservation law with monotone initial data
✍ Scribed by Matthias Kunik
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 392 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
Abstract
In this paper we prove an explicit representation formula for the solution of a one‐dimensional hyperbolic conservation law with a non‐convex flux function but monotone initial data. This representation formula is similar to those of Lax [10] and Kunik [7,8] and enables us to compute the solution pointwise explicitly. This result is a generalization of a theorem given in Kunik [8] where the case of only one inflexion point for the fluxes was considered. Its proof uses the polygonal method of Dafermos [2]. The application of this method leads to a simple explicit construction of the solutions for a Kynch sedimentation process [9] and to an explicit parameter representation for the shock curves evolving during the sedimentation process.