Abstract
In the present article, the author deals with the asymptotic stability issue of traveling wave solutions or shock waves to a simplified model of radiating gas called the Hamer model. If the shock strength, defined by the difference of the two asymptotic values, exceeds a certain threshold, the shock profiles have discontinuities of the first kind. We prove that all subcritical shock waves are stable to small perturbations due to smoothing effect of radiation, while in the critical case, arbitrary small perturbations could cause blowup in a finite time. In the supercritical cases, however, convection contributes to the recovery of stability under the presence of discontinuity in the asymptotic state. This article basically reviews the author’s two papers (Ohnawa, SIAM J Math Anal 46:2136–2159, 2014, [15]) and (Ohnawa, SIAM J Math Anal 48:3820–3839, 2016, [16]).
Published Version
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