Abstract
We study the stability and asymptotic behavior of transitional shock waves as solutions of a parabolic system of conservation laws. In contrast tp classical shock waves, transitional shock waves are semitive to the precise form of the parabolic term, not only in their internal structure but also in terms of the end states that they connect. In our numerical investigation, these waves exbibit robust stability. Moreover, their response to perturbation differs from that of classical waves; in particular, the asymptotic state of a perturbed transitional wave depends on the location of the perturbation relative to the shock wave. We develop a linear scattering model that predicts behavior agreeing quantitatively with our numerical results.
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