| Abstract: |
| We provide examples of sustained oscillations for hyperbolic-parabolic systems.
The existence of sustained oscillations in hyperbolic-parabolic system is studied systematically via examples,
for paradigm systems from viscoelasticity and for the compressible Navier-Stokes system with non-monotone pressures.
In several space dimensions oscillatory examples are associated with lack of rank-one convexity
of the stored energy.
The subject naturally leads to the problem of deriving effective equations for the associated homogenization problems.
We address that in a context of a simple one-dimensional model be addressed by employing ideas from the
kinetic formulation for conservation laws. |
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