The instant-response limit in Whitham’s nonlinear traffic-flow model: Uniform well-posedness and global existence. (English) Zbl 0685.35099

This paper presents a solution of Whitham’s traffic flow equation which are shown to exist globally in time for small values of the response-time parameter, provided that the parameter vanishes more rapidly than the cube of the diffusion parameter. It is shown that as the response time vanishes the solution converges to the entropy weak solution of the simplified equations.
Reviewer: P.K.Mahanti


35Q99 Partial differential equations of mathematical physics and other areas of application
90B20 Traffic problems in operations research
35L60 First-order nonlinear hyperbolic equations
35A35 Theoretical approximation in context of PDEs