# Optimal resource control in reaction diffusion advection population model

## TL;DR

This paper studies optimal resource control in a reaction-diffusion-advection population model, establishing existence, uniqueness, and characterization of optimal controls, supported by numerical simulations under various boundary conditions.

## Contribution

It introduces a new optimal control framework for a reaction-diffusion-advection population model with resource management, including existence and uniqueness results.

## Key findings

- Optimal control exists and is unique.
- Characterization of the optimal control is provided.
- Numerical simulations demonstrate control strategies under different boundary conditions.

## Abstract

This paper is to investigate the control problem of maximizing the net benefit of a single species while the cost of the resource allocation is minimized in a population model which can be described by a reaction diffusion advection equation of logistic type with spatial-temporal resource control coefficient. The existence of an optimal control is established and the uniqueness and characterization of the optimal control are investigated. Numerical simulation illustrate several cases with Dirichlet and Neumann boundary conditions.