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On impulsive reaction-diffusion models in higher dimensions
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- Author(s) / Creator(s)
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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 -
- Date created
- 2017-01-01
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- Type of Item
- Article (Published)