Solvability of a free-boundary problem describing the traffic flows

• Main Authors: Anvarbek Meirmanov, Sergey Shmarev, Akbota Senkebaeva
• Format: Article
• Language: English
• Published: Texas State University 2015-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Traffic flows; gas dynamics; free boundary problem
• Online Access: http://ejde.math.txstate.edu/Volumes/2015/74/abstr.html

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.