Optimal Control of Reaction Diffusion Equations with Potential Application to Biomedical Systems
In this paper we consider control problems for a class of reaction diffusion equations with polynomial nonlinearities. We prove existence of mild solutions under the assumption that the nonlinear term is strongly coercive. Next we relax this assumption and consider the natural state space for diffusion and prove existence of mild solutions locally. Using these existence results we formulate some optimal control problems and prove existence of optimal controls. Following this we develop necessary conditions of optimality. Then we consider a class of population problems, as special case of the general reaction diffusion equations, and apply optimal control theory to immunotherapy whereby physicians can determine the optimal strategy for drug administration to cancer patients.