A Remark on the Stability of Viscous Shock Waves

Abstract

Recently, Szepessy and Xin gave a new proof of stability of viscous shock waves. A curious aspect of their argument is a possible disturbance of zero mass, but $\log (t)t^{{{ - 1} /2}} $ amplitude in the vicinity of the shock wave. This would represent a previously unobserved phenomenon. However, only an upper bound is established in their proof. Here, we present an example of a system for which this phenomenon can be verified by explicit calculation. The disturbance near the shock is shown to be precisely of order $t^{{{ - 1} /2}} $ in amplitude.