Optimal control of advective direction in reaction-diffusion population models

We investigate optimal control of the advective coefficient in a class ofparabolic partial differential equations, modeling a population withnonlinear growth. This work is motivated by the question: Does movement towarda better resource environment benefit a population?Our objective functional is formulated with interpreting 'benefit'as the total population size integrated over our finite time interval.Results on existence, uniqueness, and characterization of the optimalcontrol are established. Our numerical illustrations for several growth functions and resourcefunctions indicate that movement along the resource spatial gradient benefits the population, meaningthat the optimal control is close to the spatial gradient of theresource function.