Global solutions for an extended macroscopic model for traffic flow

Abstract In this short paper, we are concerned with a nonlinear hyperbolic conservation system of three equations, which is an extended macroscopic model for traffic flow. The main contribution is to prove the global existence of weak solutions and obtain a new application of the compactness framework given in the paper “Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type” (J. Funct. Anal., 261(2011), 2797–2815).