On the well-posedness of the Cauchy problem for the generalized Korteweg-de Vries-Burgers equation
| dc.creator | Xue, Ruying | |
| dc.date | 2007-06-21 | |
| dc.date.accessioned | 2026-07-07T08:11:31Z | |
| dc.date.available | 2026-07-07T08:11:31Z | |
| dc.description | Considered is the generalized Korteweg-de Vries-Burgers equation $$ u_{t}+u_{xxx}+uu_{x}+|D_{x}|^{2α}u=0,\quad t\in \mathbb{R}^{+}, x\in \mathbb{R}, $$ with $0\leq α\le 1$. We prove a sharp results on the associated Cauchy problem in the Sobolev space $ {H}^s(\mathbb{R})$. For $s>-\min\{\frac {3+2α}4, 1\}$ we give the well-posedness of solutions of the Cauchy problem, while for $\frac 12\leα\le 1$ and for $s<-\min\{\frac {3+2α}4, 1\}$ we show some ill-posedness issues. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0706.3091 | |
| dc.identifier | http://arxiv.org/abs/0706.3091 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132143 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53; 35Q60 | |
| dc.title | On the well-posedness of the Cauchy problem for the generalized Korteweg-de Vries-Burgers equation | |
| dc.type | text |