Electron. J. Diff. Eqns.,
Vol. 2001(2001), No. 14, pp. 1-18.
###
stability of conservation laws for a traffic flow model

Tong Li

**Abstract:**

We establish the
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
topology.
We construct a functional
for two solutions which is equivalent to the
distance
between the solutions. We prove that the functional
decreases in time which yields the
well-posedness of the Cauchy
problem.
We thus obtain the
-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
norm. That is, the entropy solution with initial data as certain
-bounded
perturbations of an equilibrium shock wave exists globally and
tends to a shifted equilibrium shock wave in
norm as
.
We also show that if the initial data
is bounded and of compact
support,
the entropy solution converges in
to an equilibrium
-wave as
.
Submitted June 2, 2000. Published February 20, 2001.

Math Subject Classifications: 5L65, 35B40, 35B50, 76L05, 76J10.

Key Words: Relaxation, shock, rarefaction, L^1-contraction,
traffic flows, anisotropic, equilibrium, marginally stable,
zero relaxation limit, large-time behavior, L^1-stability.

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Tong Li

Department of Mathematics, University of Iowa

Iowa City, IA 52242, USA

e-mail: tli@math.uiowa.edu

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