Pointwise Green function bounds and long-time stability of large-amplitude noncharacteristic boundary layers

TL;DR

This paper derives precise Green function bounds for large-amplitude boundary layers in conservation laws, establishing their stability through Evans function conditions, extending previous small-amplitude results.

Contribution

It introduces sharp pointwise Green function bounds for large-amplitude boundary layers, linking stability to Evans function criteria, and extends small-amplitude stability results to the large-amplitude case.

Findings

Green function bounds are sharp and global.

Linear and nonlinear stability are equivalent to Evans function conditions.

Results extend stability analysis to large amplitudes.

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.