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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 $R^N$

J. Húska 1, and  Peter Poláčik 1,

1. 

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

Received  January 2007 Revised  June 2007 Published  October 2007

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