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Solutions and constrained null-controllability for a differential-difference equation

  • Valentina Iakovleva EMAIL logo , Raúl Manzanilla EMAIL logo , Luis Gerardo Mármol EMAIL logo and Carmen J. Vanegas EMAIL logo
Published/Copyright: May 2, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

A formula for the solution of a differential-difference equation is given, and then the corresponding semigroup theory is developed, with a detailed description of the infinitesimal generator and some of its spectral properties.

Results in Sections 2 and 3 are used in particular to show how the equation can be rewritten as a classical Cauchy problem. This, in Section 4, allows to study its exact null-controllability, by using some techniques from Functional Analysis and Operator Theory. The control u is constrained to lie in a separable weakly compact subset Ω of an arbitrary Banach space U.

Keywords: functional partial differential equations; mixed-type difference-differential equations; strongly continuous semigroups; exact controllability
MSC: Primary 34K05; 93B05

  1. This paper has been communicated by Michal Fečkan

References

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Received: 2013-4-13
Accepted: 2013-10-6
Published Online: 2016-5-2
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0127
Keywords for this article
functional partial differential equations; mixed-type difference-differential equations; strongly continuous semigroups; exact controllability

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