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

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January 2008, 20(1): 81-113. doi: 10.3934/dcds.2008.20.81

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

1.	School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Received January 2007 Revised June 2007 Published October 2007

Abstract
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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.

Keywords: principal Floquet bundle., exponential separation, Parabolic equations on $R^N$, positive entire solutions.

Mathematics Subject Classification: 35K15, 35B05, 35B4.

Citation: J. Húska, Peter Poláčik. Exponential separation and principal Floquet bundles for linear parabolic equations on $R^N$. Discrete & Continuous Dynamical Systems - A, 2008, 20 (1) : 81-113. doi: 10.3934/dcds.2008.20.81

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