Geodesic
Solvability of a free-boundary problem describing the traffic flows
Electronic journal of differential equations, Tome 2015 (2015)
We study a mathematical model of the vehicle traffic on straight freeways, which describes the traffic flow by means of equations of one-dimensional motion of the isobaric viscous gas. The corresponding free boundary problem is studied by means of introduction of Lagrangian coordinates, which render the free boundary stationary. It is proved that the equivalent problem posed in a time-independent domain admits unique local and global in time classical solutions. The proof of the local in time existence is performed with standard methods, to prove the global in time existence the system is reduced to a system of two second-order quasilinear parabolic equations.
Classification : 35B27, 46E35, 76R99
Keywords: traffic flows, gas dynamics, free boundary problem 
@article{EJDE_2015__2015__a81,
     author = {Meirmanov,  Anvarbek and Shmarev,  Sergey and Senkebaeva,  Akbota},
     title = {Solvability of a free-boundary problem describing the traffic flows},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1515.35367},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a81/}
}
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Meirmanov,  Anvarbek; Shmarev,  Sergey; Senkebaeva,  Akbota. Solvability of a free-boundary problem describing the traffic flows. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a81/