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

Mathematics – Analysis of PDEs

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

5 pages

Scientific paper

In 1992, P. Pol\'{a}\v{c}ik\cite{P2} showed that one could linearly imbed any vector fields into a scalar semi-linear parabolic equation on $\Omega$ with Neumann boundary condition provided that there exists a smooth vector field $\Phi=(\phi_{1},...,\phi_{n}) $ on $\bar{\Omega}$ such that \[ \left\{\begin{array} [c]{l}% \operatorname*{rank}(\Phi(x) ,\partial_{1}\Phi(x) ,...,\partial_{n}\Phi(x)) =n\text{for all}x\in\bar{\Omega}, \frac{\partial\Phi}{\partial\nu}=0\text{on}\partial\Omega\text{.}% \end{array} \right. \] In this short note, we give a classification of all the domains on which one may find such type of vector fields.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-378706

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.