Exponential separation and principal Floquet bundles for linear parabolic equations on general bounded domains: divergence case

Abstract

We consider the Dirichlet problem for linear nonautonomous second order parabolic equations of divergence type on general bounded domains with coefficients satisfying suitable integrability conditions. Under such minimal regularity assumptions, we establish the existence of a principal Floquet bundle exponentially separated from a complementary invariant bundle. We also prove the uniqueness of positive entire solutions in the class of solutions whose supremum norms do not grow superexponentially as time goes to negative infinity.