| Abstract: |
| This talk concerns the monostable reaction-diffusion logistic equation, which arises in mathematical biology, and a spatially discretized multi-patch model. The reaction-diffusion logistic equation, also known as the Fisher-KPP equation, has been studied extensively since its introduction as a population-dynamics model (e.g., Skellam, 1951). We focus on optimal resource-allocation strategies that maximize population persistence under a fixed total amount of resources. In particular, we consider environments in which habitat quality (or resource availability) changes sign in a spatially heterogeneous manner. This leads us to study the linearized eigenvalue problem at the trivial steady state and to determine the allocation that maximizes the population's persistence. We prove that any global maximizer of the principal eigenvalue is always of bang-bang type, and this conclusion holds independently of the underlying network structure. |
|