Control or a nonlinear thermal system via internal areas

In this paper we are concerned with the problem of controlling the state evolution of a thermal system where the control variables are in internal areas of the system domain. The system is governed by the nonlinear heat equation which is approximated numerically by means of a finite element method of first order in space and an implicit scheme in time. The descretized state equation is solved by the Newton method and the descretized control problem by the descent method. Numerical results are given in simulation for a simple example.<
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