Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations

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Abstract

We consider the Dirichlet problem for linear nonautonomous second order parabolic equations with bounded measurable coefficients on bounded Lipschitz domains. Using a new Harnack-type inequality for quotients of positive solutions, we show that each positive solution exponentially dominates any solution which changes sign for all times. We then examine continuity and robustness properties of a principal Floquet bundle and the associated exponential separation under perturbations of the coefficients and the spatial domain.

Original languageEnglish (US)
Pages (from-to)711-739
Number of pages29
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume24
Issue number5
DOIs
StatePublished - Jan 1 2007

Keywords

  • Exponential separation
  • Harnack inequalities
  • Perturbations
  • Positive entire solutions
  • Principal Floquet bundle
  • Robustness

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