A LWR model with constraints at moving interfaces. (English) Zbl 1492.35164
Summary: We propose a mathematical framework to the study of scalar conservation laws with moving interfaces. This framework is developed on a LWR model with constraint on the flux along these moving interfaces. Existence is proved by means of a finite volume scheme. The originality lies in the local modification of the mesh and in the treatment of the crossing points of the trajectories.
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35L03 | Initial value problems for first-order hyperbolic equations |
| 76A30 | Traffic and pedestrian flow models |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
hyperbolic scalar conservation laws; moving interfaces; flux constraints; finite volume schemeReferences:
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