Parameter identification for a class of abstract nonlinear parabolic distributed parameter systems
The paper deals with nonlinear parabolic evolution systems in the form \[ \begin{aligned} \frac{dy(t,q)}{dt} + A(t,q)y(t,q) &= f(t,q;y(t,q)), \quad \text{ in } (0,T), \\ y(0,q)&= y_0, \quad \text{ on } \Omega, \end{aligned} \] where \(A\) is a time-dependent differential operator and \(q\in Q\) are (unknown) real parameters. Aiming at the best approximation to the parameter \(q\) associated to the system observed states, regularity properties of the mapping between the parameter and the solution spaces allow proving existence for these so-called optimal parameters. Associated optimality conditions are deduced for the problems of both distributed and of terminal measurements (observation). In other words, the problems considered are: determine the best approximation for the system parameters when one has knowledge of the state solution in the whole time interval or just at final time, given the initial conditions.
scientific article; zbMATH DE number 2153527