The optimal control applied to diffusion-reaction models

摘要

In Ecology the Diffusion-Reaction models are widely used. The term Reaction is applied in process of growth or interaction among species in absence of dispersion, and the Diffusion describe the movement of individuals. In this work, it is modelled how an inhibitor that is deposited in the surface of rat cortex spreads to avoid the massive destruction of neurones, when, for example a brain-vascular accident occurs. The solution of the resultant non-linear diffusion-reaction equation is obtained by means of the Adomian's method. The parameters of the equation of the model are identified by using a new method that uses α-dense curves. Finally, the problem of optimal control related to this model of diffusion is considered.