Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 57, pp. 1-20.
Title: Nonlinear stability of centered rarefaction waves of the
Jin-Xin relaxation model for $2 \times 2$ conservation laws
Author: Wei-Cheng Wang (National Tsing Hua Univ., HsinChu, Taiwan)
Abstract:
We study the asymptotic equivalence of the Jin-Xin relaxation model
and its formal limit for genuinely nonlinear $2\times 2$ conservation
laws. The initial data is allowed to have jump discontinuities
corresponding to centered rarefaction waves, which includes
Riemann data connected by rarefaction curves.
We show that, as long as the initial data is a small perturbation
of a constant state, the solution for the relaxation system exists
globally in time and converges, in the zero relaxation limit,
to the solution of the corresponding conservation law uniformly
except for an initial layer.
Submitted March 15, 2002. Published June 18, 2002.
Math Subject Classifications: 65M12, 35L65.
Key Words: Jin-Xin relaxation model; conservation laws;
centered rarefaction wave.