Nonlinear Stability of Strong Planar Rarefaction Waves for the Relaxation Approximation of Conservation Laws in Several Space Dimensions

AbstractIn this paper, we show that a strong planar rarefaction wave is nonlinear stable, namely it is an attractor for the relaxation approximation of the scalar conservation laws in several space dimensions. Compared with former results obtained by T. P. Liu (1987, Comm. Math. Phys.108, 153–175) and T. Luo (1997, J. Differential Equations133, 255–279), our main novelty lies in the fact that the planar rarefaction waves do not need to be small, and in the one-dimensional case, the initial disturbance can also be chosen arbitrarily large