Instantaneous shock location and one-dimensional nonlinear stability of viscous shock wave
Analysis of PDEs
2009-09-15 v1
Abstract
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
Keywords
Cite
@article{arxiv.0909.2422,
title = {Instantaneous shock location and one-dimensional nonlinear stability of viscous shock wave},
author = {Kevin Zumbrun},
journal= {arXiv preprint arXiv:0909.2422},
year = {2009}
}