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Pointwise Green's function approach to stability for scalar conservation laws

✍ Scribed by Peter Howard

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 142 KB
Volume: 52
Category: Article
ISSN: 0010-3640
DOI: 10.1002/(sici)1097-0312(199910)52:10<1295::aid-cpa6>3.0.co;2-m

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✦ Synopsis

We study the pointwise behavior of perturbations from a viscous shock solution to a scalar conservation law, obtaining an estimate independent of shock strength. We find that for a perturbation with initial data decaying algebraically or slower, the perturbation decays in time at the rate of decay of the integrated initial data in any L p norm, p ≥ 1. Stability in any L p norm is a direct consequence. The approach taken is that of obtaining pointwise estimates on the perturbation through a Duhamel's principle argument that employs recently developed pointwise estimates on the Green's function for the linearized equation.

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