| Abstract: |
| We derive and study a spatial heterogeneous delayed reaction-diffusion equation, which models a single species with different mature-immature habitats accounting for a scenario where the boundaries are hostile to the species. We introduce new solid cones, analyze spectral bounds of several spatial heterogeneous operators, and establish limiting non-negativeness property for the whole space and the eventual comparison principle for bounded domains. As a result, we develop new domain decomposition methods so that one can compare solutions with those to associated equations from a suitable bounded spatial domain to the whole space. Then by employing domain decomposition methods and dynamical system approaches, we obtain threshold results under the supremum norm, which is greatly different from the existing results of other evolution equation in unbounded or all space. The main results are applied to two examples with the Ricker birth function and with the Mackey-Glass birth function. It reveals that the size of the immature habitat can affect the reproduction and spread of the population. This is a joint work with Dr.\ Taishan Yi. |
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