Existence and Stability of Viscoelastic Shock Profiles |
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Authors: | Blake Barker Marta Lewicka Kevin Zumbrun |
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Institution: | 1.Indiana University,Bloomington,USA;2.Department of Mathematics,University of Minnesota,Minneapolis,USA |
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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. |
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Keywords: | |
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