Journal article
L-1 stability of conservation laws for a traffic flow model
Electronic journal of differential equations, Vol.2001(14), pp.1-18
01/01/2001
Abstract
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.
We then study the large-time behavior of the entropy solutions. We show that the equilibrium shock waves are nonlinearly stable in L-1 norm. That is, the entropy solution with initial data as certain L-1 -bounded perturbations of an equilibrium shock wave exists globally and tends to a shifted equilibrium shock wave in L-1 norm as t ->infinity. We also show that if the initial data rho(0) is bounded and of compact support, the entropy solution converges in L-1 to an equilibrium N- wave as t ->+infinity.
Details
- Title: Subtitle
- L-1 stability of conservation laws for a traffic flow model
- Creators
- Tong Li
- Resource Type
- Journal article
- Publication Details
- Electronic journal of differential equations, Vol.2001(14), pp.1-18
- Publisher
- TEXAS STATE UNIV
- ISSN
- 1072-6691
- eISSN
- 1072-6691
- Number of pages
- 18
- Language
- English
- Date published
- 01/01/2001
- Academic Unit
- Mathematics
- Record Identifier
- 9984242314602771
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