We consider a conservation law on a network and generic Riemann solvers at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence Of Solutions to Cauchy problems on the whole network.
Garavello, M., Piccoli, B. (2009). Time-varying Riemann solvers for conservation laws on networks. JOURNAL OF DIFFERENTIAL EQUATIONS, 247(2), 447-464 [10.1016/j.jde.2008.12.017].
Time-varying Riemann solvers for conservation laws on networks
GARAVELLO, MAURO;
2009
Abstract
We consider a conservation law on a network and generic Riemann solvers at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence Of Solutions to Cauchy problems on the whole network.
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