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

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. [ABSTRACT FROM AUTHOR]