Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Scalar Green function bounds for instantaneous shock location and one-dimensional stability of viscous shock waves

Author: Yingwei Li
Journal: Quart. Appl. Math. 74 (2016), 499-538
MSC (2010): Primary 35-XX, 35B35
Published electronically: June 16, 2016
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Abstract: In this paper, we investigate and prove the nonlinear stability of viscous shock wave solutions of a scalar viscous conservation law, using the methods developed for general systems of conservation laws by Howard, Mascia, Zumbrun and others, based on instantaneous tracking of the location of the perturbed viscous shock wave. In some sense, this paper extends the treatment in a previous expository work of Zumbrun [``Instantaneous shock location...''] on Burgers equation to the general case, giving an exposition of these methods in the simplest setting of scalar equations. In particular we give, by a rescaling argument, a simple treatment of nonlinear stability in the small-amplitude case.

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Yingwei Li
Affiliation: Indiana University, 831 East Third Street, Rawles Hall, Bloomington, Indiana 47405
Email: YL37@umail.iu.edu

DOI: https://doi.org/10.1090/qam/1431
Received by editor(s): June 2, 2015
Published electronically: June 16, 2016
Article copyright: © Copyright 2016 Brown University

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