Solvability of a free-boundary problem describing the traffic flows
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, whic...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/74/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |