## Numerical approximation of the optimal inputs for an identification problem.(English)Zbl 0915.65069

An optimal control problem for a parabolic equation of the following form is considered: $J_\alpha(u)= {1\over 2}\cdot\| \lambda(u)- \overline\lambda\|^2_{L^2(0,T)}+{\alpha\over 2}\cdot\| u\|^2_{L^2(0,T)}\to \min,$ where $$\lambda(u)$$ is an evolutive parameter defined by $\lambda(u)(t)= u\cdot(B^*Y(u))(t)\quad\text{on }[0,T]$ with $$Y: u\to y= Y(u)$$ determined by the parabolic equation: $y_t= d\cdot\Delta y+ (Bu)(1- y)\quad\text{on}\quad Q_T:= \Omega\times (0,T),$
$y(.,0)= y_0\quad\text{on\;}\Omega,\quad y= 0\quad\text{on }\Sigma:= \Gamma\times (0,T).$ This problem is related to an identification problem. The author gives an approximation scheme and an algorithm. Some numerical results are presented.

### MSC:

 65K10 Numerical optimization and variational techniques 49M25 Discrete approximations in optimal control 49J20 Existence theories for optimal control problems involving partial differential equations
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### References:

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