Sustained Oscillations in Hyperbolic-Parabolic Systems
Analysis of PDEs
2024-10-01 v1
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.
Cite
@article{arxiv.2404.18457,
title = {Sustained Oscillations in Hyperbolic-Parabolic Systems},
author = {Athanasios E. Tzavaras},
journal= {arXiv preprint arXiv:2404.18457},
year = {2024}
}