Optimal Control of Partial Di®erential Equations and Variational Inequalities

摘要: This dissertation deals with optimal control of mathematical models described by partial differential equations and variational inequalities. It consists two parts. In the first part, a dimensional steady state thermistor problem is considered. The system nonlinear elliptic coupled some boundary conditions. conditions show how connected to its surroundings. Based on physical considerations, an objective functional be minimized introduced convective coefficient taken control. Existence uniqueness are proven. To characterize this control, optimality consisting adjoint derived. second part we consider inequality obstacle type where underlying operator biharmonic. kind arises in plasticity theory. concerns small transverse displacement plate when fixed whole subject pressure lie one side obstacle. We given solution For target profile want find such that corresponding close while norm does not get too large appropriate space. prove existence derive using approximation techniques. Namely, approximated semilinear equation approximating functional, respectively. iii