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Статья

Noncontrollability to Rest of the Two-Dimensional Distributed System Governed by the Integrodifferential Equation

Journal of Optimization Theory and Applications. 2016. Vol. 170. No. 3. P. 772-782.
Romanov I., Shamaev A.

In this paper, we examine the controllability problem of a distributed system governed by the two-dimensional Gurtin–Pipkin equation. We consider a system with compactly supported distributed control and show that if the memory kernel is a twice continuously differentiable function, such that its Laplace transformation has at least one root, then the system cannot be driven to equilibrium in finite time.