Exponential separation and principal Floquet bundles for linear parabolic equations on general bounded domains: Nondivergence case
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Abstract:
We consider the Dirichlet problem for linear nonautonomous second order parabolic equations of nondivergence type on general bounded domains with bounded measurable coefficients. Under such minimal regularity assumptions, we establish the existence of a principal Floquet bundle exponentially separated from a complementary invariant bundle. As a special case of our main theorem, assuming the coefficients are time-periodic, we obtain a new result on the existence of a principal eigenvalue of an associated (time-periodic) parabolic eigenvalue problem. We also show the existence of a uniform spectral gap between the principal eigenvalue and the rest of the spectrum for a class of time-periodic uniformly parabolic operators. Finally, we prove the uniqueness of positive entire solutions in the class of solutions whose supremum norms do not grow superexponentially as time goes to negative infinity.References
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Additional Information
- Juraj Húska
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- Email: huska@math.umn.edu
- Received by editor(s): April 26, 2006
- Published electronically: April 7, 2008
- Additional Notes: The author was supported by the Doctoral Dissertation Fellowship of the University of Minnesota
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 4639-4679
- MSC (2000): Primary 35K10; Secondary 35B05
- DOI: https://doi.org/10.1090/S0002-9947-08-04413-9
- MathSciNet review: 2403700