The generalised principal eigenvalue of time-periodic nonlocal dispersal operators and applications

Su, Yuan-Hang; Li, Wan–Tong; Lou, Yuan; Yang, Fei-Ying

doi:10.48550/arxiv.1911.08956

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2019

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“…We mention some related works [1,13,15,25,26] concerning the time-periodic nonlocal dispersal operators, where the existence and some estimates of principal eigenvalues were established. We refer to [3,4,14] for applications to evolutional dispersal in time-periodic environments.…”

Section: Introductionmentioning

confidence: 99%

Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator

Liu

Lou

Peng

et al. 2019

Proc. Amer. Math. Soc.

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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.

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