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On Traffic Flow with Nonlocal Flux: A Relaxation Representation
时间  Datetime
2019-12-13 16:00 — 17:00 
地点  Venue
Middle Lecture Room(703)
报告人  Speaker
Prof. Alberto Bressan
单位  Affiliation
The Pennsylvania State University, USA
邀请人  Host
王亚光
报告摘要  Abstract

We consider a conservation law model of traffic flow, where the velocity v of each car depends on a weighted average of the traffic density   rho(t,x)  ahead. The averaging kernel is of exponential type:  w(s)= (1/epsilon) exp(-s/ epsilon). By a transformation of coordinates, the problem can be reformulated as a 2 x 2 hyperbolic system with relaxation. Uniform BV bounds on the solution are thus obtained, independent of the scaling parameter  epsilon. As  epsilon approaches zero, the limit yields a weak solution to the corresponding conservation law  rho_t + ( rho v(rho))_x=0. In the case where the velocity  v  is affine, say   v(rho) = 1 – rho, using the Hardy-Littlewood rearrangement inequality we prove that the limit is the unique entropy-admissible solution to the scalar conservation law.