Uniqueness Result of a Two-lane Car Traffic Flow Model

The main aim of this paper is to prove a comparison result among weak solutions for a class of nonlinear parabolic systems with zero-order coupling which, in particular, describes traffic flow on long highways and assuming that the drivers continuously adjust their speed towards what they consider to be ideal value under the local traffic conditions. We develop a method based in doubling of the time variable. This technique is inspired in a method introduced by S.N. Kruzhkov [7] in order to prove a L-1-contraction property for entropy solutions of hyperbolic problems.