| Abstract: |
| In this talk, we consider the problem of maximizing the total population in a reaction-diffusion logistic model. This model has a logistic-type reaction term and a diffusion term, and the solution represents the population density distribution. This equation was proposed by J.G. Skellam in 1951 as a model for the population dynamics of organisms, and is also known as the Fisher-KPP equation. The logistic term includes a coefficient with spatial heterogeneity called the intrinsic growth rate. We show that in situations where species do not go extinct, i.e., where there is a nontrivial positive stationary solution, the total population is maximized when the intrinsic growth rate with spacial heterogeneity has a property called bang-bang type. In other words, according to this model, organisms increase their populations most when some locations are fertile and other locations are harsh. A discretized model in the relevant spatial direction will also be presented. This is a joint work with Prof. Yuan Lou and Eiji Yanagida. |
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