Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\) (Q928509)

This article deals with the perturbed heat equation \(u_t=\Delta u+ a\,u\) on the spatial domain \(\mathbb R^N\) where \(a=a(x,t)\) is an essentially bounded function. The authors give sufficient conditions which guarantee the existence of two exponentially separated Floquet bundles: a principal Floquet bundle, spanned by a positive function, and a complementary invariant bundle. The conditions include an instability assumption and a sign condition for the function \(a\). Extensions to more general linear nonautonomous second-order parabolic equations are given.