Controllability and lack of controllability with smooth controls in viscoelasticity via moment methods

Luciano Pandolfi

Controllability and lack of controllability with smooth controls in viscoelasticity via moment methods

Optimization and Control 2017-09-14 v1

Authors: Luciano Pandolfi

Abstract

In this paper we study controllability of a linear equation with persistent memory when the control belongs to $H^k_0(0,T;L^2(\ZOMq))$ . In the case the memory is zero, our equation is reduced to the wave equation and a result due to Everdoza and Zuazua informally states that smoother targets can be reached by using smoother controls. In this paper we prove that this result can be partially extended to systems with memory, but that the memory is an obstruction to a complete extensions.

Keywords

controllability viscoelasticity smooth controls moment methods wave equation persistent memory

Cite

@article{arxiv.1709.04414,
  title  = {Controllability and lack of controllability with smooth controls in viscoelasticity via moment methods},
  author = {Luciano Pandolfi},
  journal= {arXiv preprint arXiv:1709.04414},
  year   = {2017}
}

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