Instantaneous shock location and one-dimensional nonlinear stability of viscous shock wave

Details Instantaneous shock location and one-dimensional nonlinear stability of viscous shock wave Instantaneous shock location and one-dimensional nonlinear stability of viscous shock wave

2009-09-13

arxiv.org/abs/0909.2422v1

Mathematics

Analysis of PDEs

Scientific paper

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 least-squares fit pointed out by Goodman and to a simple phase condition used by Gu\`es, M\'etivier, 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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