Pointwise Green function bounds and long-time stability of large-amplitude noncharacteristic boundary layers
Analysis of PDEs
2008-02-01 v1
Abstract
Using pointwise semigroup techniques of Zumbrun--Howard and Mascia--Zumbrun, we obtain sharp global pointwise Green function bounds for noncharacteristic boundary layers of arbitrary amplitude. These estimates allow us to analyze linearized and nonlinearized stability of noncharacteristic boundary layers of one-dimensional systems of conservation laws, showing that both are equivalent to a numerically checkable Evans function condition. Our results extend to the large-amplitude case results obtained for small amplitudes by Matsumura, Nishihara and others using energy estimates.
Cite
@article{arxiv.0801.4899,
title = {Pointwise Green function bounds and long-time stability of large-amplitude noncharacteristic boundary layers},
author = {Shantia Yarahmadian and Kevin Zumbrun},
journal= {arXiv preprint arXiv:0801.4899},
year = {2008}
}
Comments
33 pp