Abstract
We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as the diffusion coefficients tend to zero, are established for non-degenerate and degenerate spatial-temporally varying environments. A new finding is the dependence of these asymptotic behaviors on the periodic solutions of a specific ordinary differential equation induced by the drift. The proofs are based upon delicate constructions of super/sub-solutions and the applications of comparison principles.
Original language | English |
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Pages (from-to) | 4895-4930 |
Number of pages | 36 |
Journal | Transactions of the American Mathematical Society |
Volume | 374 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2021 |
Externally published | Yes |