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

Fengbo Hang, Huiqiang Jiang

Research output: Contribution to journalArticle

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), ⋯, ∂ 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.

Original languageEnglish (US)
Pages (from-to)2633-2637
Number of pages5
JournalProceedings of the American Mathematical Society
Volume134
Issue number9
DOIs
StatePublished - Sep 2006

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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