Asymptotic behavior of solutions to the generalized KdV-Burgers equation with slowly decaying data
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2018
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912304094773248 |
|---|---|
| author | Fukuda, Ikki |
| author_facet | Fukuda, Ikki |
| contents | We consider the asymptotic behavior of the global solutions to the initial value problem for the generalized KdV-Burgers equation. It is known that the solution to this problem converges to a self-similar solution to the Burgers equation called a nonlinear diffusion wave. In this paper, we derive the optimal asymptotic rate to the nonlinear diffusion wave when the initial data decays slowly at spatial infinity. In particular, we investigate that how the change of the decay rate of the initial value affects the asymptotic rate to the nonlinear diffusion wave. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_07323 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of solutions to the generalized KdV-Burgers equation with slowly decaying data Fukuda, Ikki Analysis of PDEs 35B40, 35Q53 We consider the asymptotic behavior of the global solutions to the initial value problem for the generalized KdV-Burgers equation. It is known that the solution to this problem converges to a self-similar solution to the Burgers equation called a nonlinear diffusion wave. In this paper, we derive the optimal asymptotic rate to the nonlinear diffusion wave when the initial data decays slowly at spatial infinity. In particular, we investigate that how the change of the decay rate of the initial value affects the asymptotic rate to the nonlinear diffusion wave. |
| title | Asymptotic behavior of solutions to the generalized KdV-Burgers equation with slowly decaying data |
| topic | Analysis of PDEs 35B40, 35Q53 |
| url | https://arxiv.org/abs/1806.07323 |