In this paper we aim at proving well-posedness of solutions obtained as vanishing viscosity limits for the Cauchy problem on a traffic junction where $m$ incoming and $n$ outgoing roads meet. The traffic on each road is governed by a scalar conservation law $ \rho_{h,t} + f_h(\rho_h)_x = 0$, for $h\in \{1,\ldots, m+n\}$. Our proof relies upon the complete description of the set of road-wise constant solutions and its properties, which is of some interest on its own. Then we introduce a family of Kruzhkov-type adapted entropies at the junction and state a definition of admissible solution in the same spirit as in \cite{diehl, ColomboGoatinConstraint, scontrainte, AC_transmission, germes}.
Well-posedness for vanishing viscosity solutions of scalar conservation laws on a network / Andreianov, B.; Coclite, Giuseppe Maria; Donadello, C.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 37:11(2017), pp. 5913-5942. [10.3934/dcds.2017257]
Well-posedness for vanishing viscosity solutions of scalar conservation laws on a network
COCLITE, Giuseppe Maria;
2017-01-01
Abstract
In this paper we aim at proving well-posedness of solutions obtained as vanishing viscosity limits for the Cauchy problem on a traffic junction where $m$ incoming and $n$ outgoing roads meet. The traffic on each road is governed by a scalar conservation law $ \rho_{h,t} + f_h(\rho_h)_x = 0$, for $h\in \{1,\ldots, m+n\}$. Our proof relies upon the complete description of the set of road-wise constant solutions and its properties, which is of some interest on its own. Then we introduce a family of Kruzhkov-type adapted entropies at the junction and state a definition of admissible solution in the same spirit as in \cite{diehl, ColomboGoatinConstraint, scontrainte, AC_transmission, germes}.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
