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.
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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
SN - 0002-9939
VL - 134
SP - 2633
EP - 2637
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 9
ER -