Journal of Dynamics and Differential Equations

, Volume 16, Issue 2, pp 347–375

The Principal Floquet Bundle and Exponential Separation for Linear Parabolic Equations

  • Juraj Húska
  • Peter Poláčik

DOI: 10.1007/s10884-004-2784-8

Cite this article as:
Húska, J. & Poláčik, P. Journal of Dynamics and Differential Equations (2004) 16: 347. doi:10.1007/s10884-004-2784-8


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 

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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