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

Authors: Fengbo Hang and Huiqiang Jiang
Journal: Proc. Amer. Math. Soc. 134 (2006), 2633-2637
MSC (2000): Primary 35K20; Secondary 35B40, 54F65
Posted: April 7, 2006
MathSciNet review: 2213742
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Abstract | References | Similar Articles | Additional Information

Abstract: In 1992, P. Polácik showed that one could linearly imbed any vector field into a scalar semi-linear parabolic equation on $\Omega$ with Neumann boundary condition provided that there exists a smooth vector field $\Phi=\left( \phi_{1},\cdots,\phi_{n}\right)$ on $\overline{\Omega}$ such that

$\begin{displaymath} \left\{ \begin{array}[c]{l} \operatorname*{rank}\left( \Phi\... ...tial\nu}=0\text{ on }\partial\Omega\text{.} \end{array}\right. \end{displaymath}$

In this short paper, we give a classification of all the domains on which one may find such a type of vector field.

References

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