Nonlinear Stability of Centered Rarefaction Waves of the Jin-Xin Relaxation Model for 2 x 2 Conservation Laws
Southwest Texas State University, Department of Mathematics
We study the asymptotic equivalence of the Jin-Xin relaxation model and its formal limit for genuinely nonlinear 2 x 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.
Jin-Xin relaxation model, Conservation laws, Centered rarefaction wave
Wang, W. C. (2002). Nonlinear stability of centered rarefaction waves of the Jin-Xin relaxation model for $2 \times 2$ conservation laws. <i>Electronic Journal of Differential Equations, 2002</i>(57), pp. 1-20.