Sustained Oscillations in Hyperbolic-Parabolic Systems
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912049193287680 |
|---|---|
| author | Tzavaras, Athanasios E. |
| author_facet | Tzavaras, Athanasios E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sustained Oscillations in Hyperbolic-Parabolic Systems Tzavaras, Athanasios E. Analysis of PDEs 35M31, 35L65, 74H05, 74H35, 74N20 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. |
| title | Sustained Oscillations in Hyperbolic-Parabolic Systems |
| topic | Analysis of PDEs 35M31, 35L65, 74H05, 74H35, 74N20 |
| url | https://arxiv.org/abs/2404.18457 |