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.
Research of B.B. was partially supported
under NSF grant no. DMS-0801745.
Research of M.L. was partially supported
under NSF grants no. DMS-0707275 and DMS-0846996.
Research of K.Z. was partially supported
under NSF grants no. DMS-0300487 and DMS-0801745.
Barker, Blake; Lewicka, Marta; Zumbrun, Kevin.
Existence and stability of viscoelastic shock profiles.
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