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

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

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.

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

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

M3 - Article

AN - SCOPUS:33748288096

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 -