Existence and stability of viscoelastic shock profiles
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.
Keywords
Cite
@article{arxiv.1006.1665,
title = {Existence and stability of viscoelastic shock profiles},
author = {Blake Barker and Marta Lewicka and Kevin Zumbrun},
journal= {arXiv preprint arXiv:1006.1665},
year = {2015}
}
Comments
43 pages, 12 figures