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

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

2008-01-31

arxiv.org/abs/0801.4899v1

Mathematics

Analysis of PDEs

33 pp

Scientific paper

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.

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