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- Title
The particle paths of hyperbolic conservation laws.
- Authors
Fjordholm, Ulrik S.; Mæhlen, Ola H.; Ørke, Magnus C.
- Abstract
Nonlinear scalar conservation laws are traditionally viewed as transport equations. We take instead the viewpoint of these PDEs as continuity equations with an implicitly defined velocity field. We show that a weak solution is the entropy solution if and only if the ODE corresponding to its velocity field is well-posed. We also show that the flow of the ODE is 1/2-Hölder regular. Finally, we give several examples showing that our results are sharp, and we provide explicit computations in the case of a Riemann problem.
- Subjects
CONSERVATION laws (Physics); TRANSPORT equation; RIEMANN-Hilbert problems; CONSERVATION laws (Mathematics)
- Publication
Mathematical Models & Methods in Applied Sciences, 2024, Vol 34, Issue 7, p1205
- ISSN
0218-2025
- Publication type
Article
- DOI
10.1142/S0218202524500209