Instantaneous shock location and one-dimensional nonlinear stability of viscous shock waves
نویسنده
چکیده
We illustrate in a simple setting the instantaneous shock tracking approach to stability of viscous conservation laws introduced by Howard, Mascia, and Zumbrun. This involves a choice of the definition of instanteous location of a viscous shock– we show that this choice is time-asymptotically equivalent both to the natural choice of leastsquares fit pointed out by Goodman and to a simple phase condition used by Guès, Métivier, Williams, and Zumbrun in other contexts. More generally, we show that it is asymptotically equivalent to any location defined by a localized projection.
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