The Principal Floquet Bundle and Exponential Separation for Linear Parabolic Equations |
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Authors: | Juraj Húska Peter Poláčik |
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Institution: | (1) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA |
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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 |
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Keywords: | Nonautonomous parabolic equations principal Floquet bundle exponential separation positive entire solutions |
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