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|Title: ||Existence and stability of viscoelastic shock profiles|
|Authors: ||Barker, Blake|
|Issue Date: ||9-Jun-2010|
|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 or nonclassical type shock profiles.|
|Appears in Collections:||Preprints|
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