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

Iakovleva, V. A.; Manzanilla, Raúl; Mármol, Luis Gerardo; Vanegas, Carmen Judith

doi:10.1515/ms-2015-0127

Cited by 2 publications

(3 citation statements)

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“…In the same line of research to the ones presented here but considering other topological spaces that are not Banach spaces, we refer the reader to [9,10,11,12].…”

Section: Final Remarksmentioning

confidence: 99%

Delay Differential Equations in Sequence Spaces

Mármol¹,

Vanegas²

2019

Communications in Advanced Mathematical Sciences

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The standard delay equations are newly studied in the context of classical separable Banach Sequence Spaces. As a classical solution is shown to exist, the associated semigroup and its infinitesimal generator are found, and some important properties of those operators are proven, including some spectral properties. As an application, it is shown how can these results be used to characterize the constrained null-controllability.

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“…In the same line of research to the ones presented here but considering other topological spaces that are not Banach spaces, we refer the reader to [9,10,11,12].…”

Section: Final Remarksmentioning

confidence: 99%

Delay Differential Equations in Sequence Spaces

Mármol¹,

Vanegas²

2019

Communications in Advanced Mathematical Sciences

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“…The present work is an attempt to see the results in [9] and [13] in a more general context. As we have indicated, there exist other examples where a unique solution can be found ( [5], [6], [7] and [10]).…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…As far as we know, similar studies to the one presented here for this type of equations haven't been done. This type of equations are, in general, ill-posed as initial value problems (see for example, [1] and [4]), but there are also cases ( [5], [6], [7], [8], [9] and [10]) where a unique differentiable solution exists. We make the statement of the problem in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach

Mármol¹,

Vanegas²

2018

Communications in Advanced Mathematical Sciences

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In this paper we study certain systems of mixed-type functional differential equations, from the point of view of the C 0 -semigroup theory. In general, this type of equations are not well-posed as initial value problems. But there are also cases where a unique differentiable solution exists. For these cases and in order to achieve our goal, we first rewrite the system as a classical Cauchy problem in a suitable Banach space. Second, we introduce the associated semigroup and its infinitesimal generator and prove important properties of these operators. As an application, we use the results to characterize the null controllability for those systems, where the control u is constrained to lie in a non-empty compact convex subset Ω of R n .

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

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

Cited by 2 publications

References 10 publications

Delay Differential Equations in Sequence Spaces

Delay Differential Equations in Sequence Spaces

Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach

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