Electron. J. Diff. Equ., Vol. 2015 (2015), No. 74, pp. 1-12.

Solvability of a free-boundary problem describing the traffic flows

Anvarbek Meirmanov, Sergey Shmarev, Akbota Senkebayeva

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.

Submitted February 19, 2015. Published March 24, 2015.
Math Subject Classifications: 35B27, 46E35, 76R99.
Key Words: Traffic flows; gas dynamics; free boundary problem.

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Anvarbek Meirmanov
Kazakh-British Technical University
Tole Bi 59, Almaty, Kazakhstan
email: anvarbek@list.ru
Akbota Senkebayeva
Kazakh-British Technical University
Tole Bi 59, Almaty, Kazakhstan
email: akbota.senkebayeva@gmail.com
Sergey Shmarev
Department of Mathematics, University of Oviedo
c/Calvo Sotelo s/n, 33007
Oviedo, Spain
email: shmarev@uniovi.es

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