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Scalar Green Function Bounds for Instantaneous Shock Location and One-dimensional Stability of Viscous Shock Waves

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 نشر من قبل Yingwei Li
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English
 تأليف Yingwei Li




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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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