<p>This paper is devoted to the study of the threshold dynamics for a class of time-delayed reaction diffusion equations in a time-periodic shifting environment which is suitable for survival only in bounded regions. We first establish the spreading properties of solutions under the assumption of uniform asymptotic annihilation. Then we prove a threshold type result on forced time-periodic waves in terms of asymptotic spectral radius. We also obtain a set of sufficient conditions for the uniqueness and stability of such time-periodic waves. At last, we give a lower bound estimate for the asymptotic spectral radius via a Dirichlet boundary value problem.</p>

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Threshold Dynamics for a Class of Time-Delayed Reaction Diffusion Equations in a Periodic Shifting Habitat

  • Leyi Jiang,
  • Xiao-Qiang Zhao

摘要

This paper is devoted to the study of the threshold dynamics for a class of time-delayed reaction diffusion equations in a time-periodic shifting environment which is suitable for survival only in bounded regions. We first establish the spreading properties of solutions under the assumption of uniform asymptotic annihilation. Then we prove a threshold type result on forced time-periodic waves in terms of asymptotic spectral radius. We also obtain a set of sufficient conditions for the uniqueness and stability of such time-periodic waves. At last, we give a lower bound estimate for the asymptotic spectral radius via a Dirichlet boundary value problem.