A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations
| dc.creator | Hang, Fengbo | |
| dc.creator | Jiang, Huiqiang | |
| dc.date | 2006-10-25 | |
| dc.date.accessioned | 2026-07-07T07:29:25Z | |
| dc.date.available | 2026-07-07T07:29:25Z | |
| dc.description | In 1992, P. Poláčik\cite{P2} showed that one could linearly imbed any vector fields into a scalar semi-linear parabolic equation on $Ω$ with Neumann boundary condition provided that there exists a smooth vector field $Φ=(ϕ_{1},...,ϕ_{n}) $ on $\barΩ$ such that \[ \left\{\begin{array} [c]{l}% \operatorname*{rank}(Φ(x) ,\partial_{1}Φ(x) ,...,\partial_{n}Φ(x)) =n\text{for all}x\in\barΩ, \frac{\partialΦ}{\partialν}=0\text{on}\partialΩ\text{.}% \end{array} \right. \] In this short note, we give a classification of all the domains on which one may find such type of vector fields. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610764 | |
| dc.identifier | http://arxiv.org/abs/math/0610764 | |
| dc.identifier | Proceedings of AMS, 134(9):2633-2637, 2006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118103 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Dynamical Systems | |
| dc.subject | Primary 35K20; Secondary 35B40, 54F65 | |
| dc.title | A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations | |
| dc.type | text |