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arXiv · 2404.18457

Sustained Oscillations in Hyperbolic-Parabolic Systems

Athanasios E. Tzavaras
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Abstract

We construct examples of oscillating solutions with persistent oscillations for various hyperbolic-parabolic systems with singular diffusion matrices that appear in mechanics. These include, an example for the equations of nonlinear viscoelasticity of Kelvin-Voigt type with stored energy that violates rank-one convexity, which amounts to a time-dependent variant of twinning solutions. An example pertaining to the system of gas dynamics with thermal effects for a viscous, adiabatic gas. Finally, an example for the compressible Navier-Stokes system in one-space dimension with nonmonotone pressure function. We also study the existence of oscillating solutions for linear hyperbolic-parabolic systems with singular diffusion matrices.

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Athanasios E. Tzavaras. 2024-04-29. Sustained Oscillations in Hyperbolic-Parabolic Systems. https://arxiv.org/abs/2404.18457

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