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 instantaneous location of a viscous shock. We show that this choice is time-asymptotically equivalent both to the natural choice of least-squares 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.
CITATION STYLE
Zumbrun, K. (2011). Instantaneous shock location and one-dimensional nonlinear stability of viscous shock waves. Quarterly of Applied Mathematics, 69(1), 177–202. https://doi.org/10.1090/s0033-569x-2011-01221-6
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