Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 74, pp. 112.
Solvability of a freeboundary problem describing the traffic flows
Anvarbek Meirmanov, Sergey Shmarev, Akbota Senkebaeva
Abstract:
We study a mathematical model of the vehicle traffic on straight freeways,
which describes the traffic flow by means of equations of onedimensional
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 timeindependent 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 secondorder 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
KazakhBritish Technical University
Tole Bi 59, Almaty, Kazakhstan
email: anvarbek@list.ru


Akbota Senkebaeva
KazakhBritish 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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