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The Principal Floquet Bundle and Exponential Separation for Linear Parabolic Equations

  • Juraj Húska
  • Peter Poláčik
Article

Abstract

We consider linear nonautonomous second order parabolic equations on bounded domains subject to Dirichlet boundary condition. Under mild regularity assumptions on the coefficients and the domain, we establish the existence of a principal Floquet bundle exponentially separated from a complementary invariant bundle. Our main theorem extends in a natural way standard results on principal eigenvalues and eigenfunctions of elliptic and time-periodic parabolic equations. Similar theorems were earlier available only for smooth domains and coefficients. As a corollary of our main result, we obtain the uniqueness of positive entire solutions of the equations in

Nonautonomous parabolic equations principal Floquet bundle exponential separation positive entire solutions 

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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • Juraj Húska
    • 1
  • Peter Poláčik
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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