The existence of global BV solutions for the Aw-Rascle system with linear damping is considered. In order to get approximate solutions we consider the system in Lagrangian coordinates, then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of [1] we get a sequence of approximate solutions. Finally we show the convergence of this approximate sequence to the weak entropic solution.
Juan C. JUAJIBIOY
. ON THE CAUCHY PROBLEM FOR AW-RASCLE SYSTEM WITH LINEAR DAMPING[J]. Acta mathematica scientia, Series B, 2021
, 41(1)
: 311
-318
.
DOI: 10.1007/s10473-021-0118-0
[1] Goatin P, Laurent-Brouty N. The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model. Z Angen Math Phys, 2019, 70(31):1-24
[2] Aw A, Rascle M. Resurrection of "second order" models of traffic flow. SIAM J Appl Math, 2000, 60(3):916-938
[3] Godvik M, Hanche-Olsen H. Existence of solutions for the Aw-Rascle traffic flow model with vacuum. J Hyperbolic Differ Equ, 2008, 5(1):45-63
[4] Lu Y G. Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type. J Funct Anal, 2011, 261(10):2797-2815
[5] Peng Y J. Euler Lagrange change of variables in conservation laws. Nonlinearity, 2007, 20(8):1927-1953
[6] Crasta G, Piccoli B. Viscosity solutions and uniqueness for systems of inhomogeneous balance laws. Discrete Continuous Dyn Syst, 1997, 3(4):477-502
[7] Baiti P, Bressan A. The semigroup generated by a temple class system with large data. Diff Integr Equ, 1997, 10(3):401-418
[8] Hoff D. Invariant regions for systems of conservation laws. Trans Amer Math Soc, 1985, 289(2):591-610
[9] Chueh K N, Conley C C, Smoller J A. Positively invariant regions for systems of nonlinear diffusion equations. Indiana Univ Math J, 1985, 26(2):373-392
[10] Bressan A. Hyperbolic System of Conservation Laws:The One-Dimensional Cauchy Problem. Oxford:Oxford University Press, 2000
