L∞-stability of discontinuous traveling waves in a radiating gas model

Abstract

In the present article, we prove the L∞-stability of discontinuous or supercritical shock waves which appear in a model system of radiating gases if the shock strength is greater than a certain critical value. The author has recently shown (SIAM J. Math. Anal. (2014), 2136–2159.) that all subcritical shockwaves are stable to small perturbations while the critical shock wave blows up the first order derivative in a finite time if certain types of perturbations are added whatever small the perturbations may be. In the supercritical case, we show that the convection contributes to recover the stability by virtue of discontinuity in the asymptotic state compensating the insufficient smoothing effect of radiation.