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

Igor Romanov and Alexey Shamaev
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Alexey Shamaev: Institute for Problems in Mechanics RAS

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 3, No 4, 772-782

Abstract: Abstract 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.

Keywords: Lack of controllability to rest; Equation with memory; Distributed control; Moment problems; 45K05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0945-7

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