### Adam Kowalewski (AGH University of Science and Technology, Kraków, Poland)

#### Optimal control of parabolic systems with delays

*Friday 24 November 2017 at 14.00, JCMB 5326*

##### Abstract

We consider an optimal boundary control problem for a linear parabolic system
in which time delays appear in the integral form with *k ∈ (0,c)* in
the state equation and with *h ∈ (0,b)* in the Neumann boundary
condition.

Sufficient conditions for the existence of a unique solution for such
parabolic system are presented. The performance functionals have quadratic
form. The time horizon *T* is fixed. Finally, we impose some constraints
on the boundary control. Making use of Lion's framework necessary and
sufficient conditions of optimality are derived for a linear quadratic problem.

A simple example of application is also provided.

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