L^1 stability of conservation laws for a traffic flow model

Electronic Journal of Differential Equations

关键词: Relaxation;    shock;    rarefaction;    $L^1$-contraction;    traffic flows;    anisotropic;    equilibrium;    marginally stable;    zero relaxation limit;    large-time behavior;    $L^1$-stability.;   

DOI  :  

来源: DOAJ

【 摘 要 】

We establish the $L^1$ well-posedness theory for a system of nonlinear hyperbolic conservation laws with relaxation arising in traffic flows. In particular, we obtain the continuous dependence of the solution on its initial data in $L^1$ topology. We construct a functional for two solutions which is equivalent to the $L^1$ distance between the solutions. We prove that the functional decreases in time which yields the $L^1$ well-posedness of the Cauchy problem. We thus obtain the $L^1$-convergence to and the uniqueness of the zero relaxation limit.

【 授权许可】

Unknown