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| Title: | Existence and stability of viscoelastic shock profiles |
| Authors: | Barker, Blake
Lewicka, Marta
Zumbrun, Kevin |
| 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. |
| Permanent URL: | http://purl.umn.edu/90859 |
| Appears in Collections: | Preprints
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| BLZ62.pdf | | 648Kb | PDF | View/Open |
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