On impulsive reaction-diffusion models in higher dimensions

  • Author(s) / Creator(s)
  • We formulate a general impulsive reaction-diffusion equation model to describe
    the population dynamics of species with distinct reproductive and dispersal stages. The seasonal
    reproduction is modeled by a discrete-time map, while the dispersal is modeled by a reaction-diffusion
    partial differential equation. Study of this model requires a simultaneous analysis of the differential
    equation and the recurrence relation. When boundary conditions are hostile we provide critical
    domain results showing how extinction versus persistence of the species arises, depending on the size
    and geometry of the domain. We show that there exists an extreme volume size such that if |Ω| falls
    below this size the species is driven extinct, regardless of the geometry of the domain. To construct
    such extreme volume sizes and critical domain sizes, we apply Schwarz symmetrization rearrangement
    arguments, the classical Rayleigh–Faber–Krahn inequality, and the spectrum of uniformly elliptic
    operators. The critical domain results provide qualitative insight regarding long-term dynamics for
    the model. Last, we provide applications of our main results to certain biological reaction-diffusion
    models regarding m

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    Article (Published)
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    Attribution-NonCommercial 4.0 International