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 language||English (US)|
|Number of pages||29|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - 2007|
Bibliographical noteFunding Information:
* Corresponding author. E-mail addresses: firstname.lastname@example.org (J. Húska), email@example.com (P. Polácˇik), firstname.lastname@example.org (M.V. Safonov). 1 Supported in part by NSF Grant DMS-0400702.
- Exponential separation
- Harnack inequalities
- Positive entire solutions
- Principal Floquet bundle