Optimality conditions for a class of distributed parameter system

摘要

In ref., Casas considers the system governed by linear elliptic equation, which involves control in coefficient, and the phase space of control is convex and the cost functional is convex. Casas obtained the necessary conditions of optimal control byusing convex analysis theories. In this note, the phase space of control is not convex and the cost functional may not be convex. We will give the necessary conditions of optimal control using the convexification method and Ekeland variational principle. We point out that problems (1)--(3) have very much application in materials science and engineering technology. For example, they may be used in problems of composition of material.