Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2401.03696 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909064752005120 |
|---|---|
| author | Chang, lin Liu, Duo Zhang, Weiqiang |
| author_facet | Chang, lin Liu, Duo Zhang, Weiqiang |
| contents | In this paper, a rarefaction wave under space-periodic perturbation for the 3 times 3 rate-type viscoelastic system is considered. It is shown that if the initial perturbation around the rarefaction wave is suitably small, then the solution of the rate-type viscoelastic system tends to the rarefaction wave. The stability of solutions under periodic perturbations is an interesting and important problem since the perturbation keeps oscillating at the far fields. That is, the perturbation is not integral in space. The key of proof is to construct a suitable ansatz carrying the same oscillation as the solution. Then we can find cancellations between solutions and ansatz such that the perturbation belongs to some Sobolev space. The nonlinear stability can be obtained by the weighted energy method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of Rarefaction Waves Under Periodic Perturbation for A Rate-Type Viscoelastic System Chang, lin Liu, Duo Zhang, Weiqiang Analysis of PDEs In this paper, a rarefaction wave under space-periodic perturbation for the 3 times 3 rate-type viscoelastic system is considered. It is shown that if the initial perturbation around the rarefaction wave is suitably small, then the solution of the rate-type viscoelastic system tends to the rarefaction wave. The stability of solutions under periodic perturbations is an interesting and important problem since the perturbation keeps oscillating at the far fields. That is, the perturbation is not integral in space. The key of proof is to construct a suitable ansatz carrying the same oscillation as the solution. Then we can find cancellations between solutions and ansatz such that the perturbation belongs to some Sobolev space. The nonlinear stability can be obtained by the weighted energy method. |
| title | Stability of Rarefaction Waves Under Periodic Perturbation for A Rate-Type Viscoelastic System |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.03696 |