We consider a hyperbolic conservation law with discontinuous flux. Such a partial differential equation arises in different applications, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions.
Garavello, M., Natalini, R., Piccoli, B., Terracina, A. (2007). Conservation laws with discontinuous flux. NETWORKS AND HETEROGENEOUS MEDIA, 2(1), 159-179 [10.3934/nhm.2007.2.159].
Conservation laws with discontinuous flux
GARAVELLO, MAURO;
2007
Abstract
We consider a hyperbolic conservation law with discontinuous flux. Such a partial differential equation arises in different applications, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions.
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