Existence and stability of viscoelastic shock profiles

Barker, Blake
Lewicka, Marta
Zumbrun, Kevin
2010-06-09
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Existence and stability of viscoelastic shock profiles

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2010-06-09

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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.

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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.

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Barker, Blake; Lewicka, Marta; Zumbrun, Kevin. (2010). Existence and stability of viscoelastic shock profiles. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/90859.

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