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Archive for Rational Mechanics and Analysis

, Volume 200, Issue 2, pp 491–532 | Cite as

Existence and Stability of Viscoelastic Shock Profiles

  • Blake Barker
  • Marta Lewicka
  • Kevin ZumbrunEmail author
Article

Abstract

We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and Malek-Madani. We establish that the resulting equations fall into the class of symmetrizable hyperbolic–parabolic systems, hence spectral stability implies linearized and nonlinear stability with sharp rates of decay. The new contributions are treatment of the compressible case, formulation of a rigorous nonlinear stability theory, including verification of stability of small-amplitude Lax shocks, and the systematic incorporation in our investigations of numerical Evans function computations determining stability of large-amplitude and nonclassical type shock profiles.

Keywords

Nonlinear Stability Parabolic System Evans Function Viscous Stress Tensor Spectral Stability 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Indiana UniversityBloomingtonUSA
  2. 2.Department of MathematicsUniversity of MinnesotaMinneapolisUSA

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