### Abstract

In 1992, P. Poláčik showed that one could linearly imbed any vector field into a scalar semi-linear parabolic equation on Ω with Neumann boundary condition provided that there exists a smooth vector field Φ = (φ,⋯, φ _{n}) on Ω̄ such that {rank (Φ (x), ∂ _{1} Φ (x), ⋯, ∂ _{n}Φ (x)) = n for all x ε Ω̄, ∂Φ/∂ν = 0 on ∂Ω. In this short paper, we give a classification of all the domains on which one may find such a type of vector field.

Original language | English (US) |
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Pages (from-to) | 2633-2637 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 134 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2006 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations.** / Hang, Fengbo; Jiang, Huiqiang.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 134, no. 9, pp. 2633-2637. https://doi.org/10.1090/S0002-9939-06-08627-8

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TY - JOUR

T1 - A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations

AU - Hang, Fengbo

AU - Jiang, Huiqiang

PY - 2006/9

Y1 - 2006/9

N2 - In 1992, P. Poláčik showed that one could linearly imbed any vector field into a scalar semi-linear parabolic equation on Ω with Neumann boundary condition provided that there exists a smooth vector field Φ = (φ,⋯, φ n) on Ω̄ such that {rank (Φ (x), ∂ 1 Φ (x), ⋯, ∂ nΦ (x)) = n for all x ε Ω̄, ∂Φ/∂ν = 0 on ∂Ω. In this short paper, we give a classification of all the domains on which one may find such a type of vector field.

AB - In 1992, P. Poláčik showed that one could linearly imbed any vector field into a scalar semi-linear parabolic equation on Ω with Neumann boundary condition provided that there exists a smooth vector field Φ = (φ,⋯, φ n) on Ω̄ such that {rank (Φ (x), ∂ 1 Φ (x), ⋯, ∂ nΦ (x)) = n for all x ε Ω̄, ∂Φ/∂ν = 0 on ∂Ω. In this short paper, we give a classification of all the domains on which one may find such a type of vector field.

UR - http://www.scopus.com/inward/record.url?scp=33748288096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748288096&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-06-08627-8

DO - 10.1090/S0002-9939-06-08627-8

M3 - Article

VL - 134

SP - 2633

EP - 2637

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -