Exponential separation and principal floquet bundles for linear parabolic equations on ℝN

Juraj Húska, Peter Poláčik

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider linear nonautonomous second order parabolic equations on ℝN. Under an instability condition, we prove the existence of two complementary Floquet bundles, one spanned by a positive entire solution - the principal Floquet bundle, the other one consisting of sign-changing solutions. We establish an exponential separation between the two bundles, showing in particular that a class of sign-changing solutions are exponentially dominated by positive solutions.

Original languageEnglish (US)
Pages (from-to)81-113
Number of pages33
JournalDiscrete and Continuous Dynamical Systems
Volume20
Issue number1
DOIs
StatePublished - Jan 2008

Keywords

  • Exponential separation
  • Parabolic equations on ℝ
  • Positive entire solutions
  • Principal Floquet bundle

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