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

Author

Listed:
  • Igor Romanov

    (National Research University Higher School of Economics)

  • Alexey Shamaev

    (Institute for Problems in Mechanics RAS
    Lomonosov Moscow State University)

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.

Suggested Citation

  • Igor Romanov & Alexey Shamaev, 2016. "Noncontrollability to Rest of the Two-Dimensional Distributed System Governed by the Integrodifferential Equation," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 772-782, September.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:3:d:10.1007_s10957-016-0945-7
    DOI: 10.1007/s10957-016-0945-7
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