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.
RésuméOn considère le problème de Dirichlet pour des équations paraboliques linéaires non autonomes du second ordre avec coefficients bornés mesurables sur un domaine borné de Lipschitz. Utilisant une nouvelle inégalité du type Harnack pour les quotients de solutions strictement positives, on montre que toute solution positive domine exponentiellement toute solution qui change de signe en tout temps. On examine ensuite les propriétés de continuité et de robustesse pour un fibré principal de Floquet et la séparation exponentielle associée à des perturbations des coefficients et du domaine spatial.
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