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Exponential separation and principal Floquet bundles for linear parabolic equations on $R^N$

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  • We consider linear nonautonomous second order parabolic equations on $\R^N$. Under an instability condition, we prove the existence of two complementary Floquet bundles, one spanned by a positive entire solution - the principal Floquet bundle, the other one consisting of sign-changing solutions. We establish an exponential separation between the two bundles, showing in particular that a class of sign-changing solutions are exponentially dominated by positive solutions.
    Mathematics Subject Classification: 35K15, 35B05, 35B40.

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