On the Input Estimation Problem for PDE:
       the Regularized Solutions and Evolutionary Numerical Algorithms

       I. Sivergina
       Institute of Mathematics and Mechanics
       S.Kowalewski Str. 16, 620219 Ekaterinburg, Russia
       siv@oou.imm.intec.ru

The present paper is devoted to the input estimation
problem for dynamical system described by the partial differential
equation of parabolic type. The so called $H_\infty$- approach to the
deterministic treatment  of uncertainties in the system is taken.
Two issues  are treated here. The first of these is the evolutionary
procedure of estimating the input of the system. The second is the
regularization problem for the informational state of the system -
the last one is the value function in a optimization problem related to
an estimation problem under consideration.