Control problem for a non‐linear thermoelasticity system

The control problem for a three‐dimensional non‐linear thermoelasticity system is considered. The system may represent, among others, the dynamical model of shape memory materials. As controls we take distributed heat sources and body forces. The goal functional refers to the desired evolution of displacement, strain and temperature. The continuity and differentiability of solutions with respect to controls is studied. The existence of optimal controls is proved and the necessary optimality conditions are formulated. The existence of adjoint state variables is proved under additional regularity of data. Copyright © 2004 John Wiley & Sons, Ltd.