The initial boundary value problem for a class of scalar nonautonomous conservation laws in 1 space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity assumptions on the flow are extended to a merely L ∞ dependence on time. These results ensure, for instance, the well-posedness of a class of vehicular traffic models with time-dependent speed limits. A traffic management problem is then shown to admit an optimal solution.
IBVPs for scalar conservation laws with time discontinuous fluxes / Colombo, Rm; Rossi, E. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - 41:4(2018), pp. 1463-1479. [10.1002/mma.4676]
IBVPs for scalar conservation laws with time discontinuous fluxes
Rossi, E
2018
Abstract
The initial boundary value problem for a class of scalar nonautonomous conservation laws in 1 space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity assumptions on the flow are extended to a merely L ∞ dependence on time. These results ensure, for instance, the well-posedness of a class of vehicular traffic models with time-dependent speed limits. A traffic management problem is then shown to admit an optimal solution.
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