A simple PDE-constrained Optimization Problem to Evaluate the Strategy for Fishery Resource Transportation

Abstract

We present a new impulse control problem of degenerate parabolic Fokker-Planck equations that govern stochastic growth dynamics of biological resource from the viewpoint of probability density functions of the body weight. The problem we focus on is impulsively transporting a resource population from a habitat to other habitat(s), which stems from a recent engineering problem in a river in Japan. A formula of the optimal control is theoretically derived with the help of an adjoint equation method. A remarkable point is simplicity of the problem such that finding the optimal control can be achieved by only solving an adjoint equation. We present a demonstrative computational example of Ayu sweetfish Plecoglossus altivelis altivelis utilizing a very recent Weighted Essentially Non-Oscillatory method.