STABILITY OF A RELAXATION MODEL WITH A NONCONVEX FLUX

In this paper, we study the nonlinear stability of travelling wave sol utions with shock profile for a relaxation model with a nonconvex flux , which is proposed by Jin and Xin [Comm. Pure Appl. Math., 48 (1995), pp. 555-563] to approximate an original hyperbolic system numerically under the subcharacteristic condition introduced by T. P. Liu [Comm. Math. Phys., 108 (1987), pp. 153-175]. The travelling wave solutions w ith strong shock profile are shown to be asymptotically stable under s mall disturbances with integral zero using an elementary but technical energy method. Proofs involve detailed study of the error equation fo r disturbances using the same weight function introduced in [Comm. Mat h. Phys., 165 (1994), pp. 83-96].