scholarly journals Boundary Controllability of a Pseudoparabolic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qiang Tao ◽  
Hang Gao ◽  
Zheng-an Yao
Keyword(s):  
Explicit Solution ◽  
Approximate Controllability ◽  
Null Controllability ◽  
Pseudoparabolic Equation ◽  
Controllability Problem ◽  
Boundary Controllability ◽  
Boundary Controls ◽  
Controllability Property

We deal with the controllability problem for the pseudoparabolic equation by means of boundary controls. Due to the unusual spectrum of this kind of equations, we prove that the null controllability property is false. Furthermore, by the explicit solution, we show that the approximate controllability holds.

scholarly journals Null Controllability of a Nonlinear Age Structured Model for a Two-Sex Population

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Amidou Traoré ◽  
Okana S. Sougué ◽  
Yacouba Simporé ◽  
Oumar Traoré
Keyword(s):  
Null Controllability ◽  
Auxiliary System ◽  
Time Interval ◽  
Observability Inequality ◽  
Controllability Problem ◽  
Structured Model ◽  
Male And Female ◽  
System A ◽  
Age Structured ◽  
Age Structured Model

This paper is devoted to study the null controllability properties of a nonlinear age and two-sex population dynamics structured model without spatial structure. Here, the nonlinearity and the couplage are at the birth level. In this work, we consider two cases of null controllability problem. The first problem is related to the extinction of male and female subpopulation density. The second case concerns the null controllability of male or female subpopulation individuals. In both cases, if A is the maximal age, a time interval of duration A after the extinction of males or females, one must get the total extinction of the population. Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after Kakutani’s fixed-point theorem.

scholarly journals On the Exact Boundary Control for the Linear Klein-Gordon Equation in Non-cylindrical Domains

2020 ◽  
Vol 21 (2) ◽  
pp. 371
Author(s):  
R. S. O. Nunes
Keyword(s):  
Initial Data ◽  
Wave Operator ◽  
Gordon Equation ◽  
Controllability Problem ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Exact Boundary ◽  
Cylindrical Domains ◽  
Klein Gordon ◽  
Klein Gordon Equation

The purpose of this paper is to study an exact boundary controllability problem in noncylindrical domains for the linear Klein-Gordon equation. Here, we work near of the extension techniques presented By J. Lagnese in [12] which is based in the Russell’s controllability method. The control time is obtained in any time greater then the value of the diameter of the domain on which the initial data are supported. The control is square integrable and acts on whole boundary and it is given by conormal derivative associated with the above-referenced wave operator.

Lack of null controllability of viscoelastic flows

2019 ◽  
Vol 25 ◽  
pp. 60
Author(s):  
Debayan Maity ◽  
Debanjana Mitra ◽  
Michael Renardy
Keyword(s):  
Approximate Controllability ◽  
Momentum Equation ◽  
Null Controllability ◽  
Viscoelastic Flow ◽  
Viscoelastic Flows ◽  
Relaxation Mode ◽  
Maxwell Fluids ◽  
Linear Viscoelastic ◽  
Exact Null Controllability

We consider controllability of linear viscoelastic flow with a localized control in the momentum equation. We show that, for Jeffreys fluids or for Maxwell fluids with more than one relaxation mode, exact null controllability does not hold. This contrasts with known results on approximate controllability.

scholarly journals Exact null-controllability of interconnected abstract evolution equations with unbounded input operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Benzion Shklyar
Keyword(s):  
Evolution Equations ◽  
Null Controllability ◽  
Current Paper ◽  
Interconnected Systems ◽  
Controllability Problem ◽  
Abstract Evolution Equations ◽  
Smooth Controls ◽  
Distributed Controls ◽  
Exact Null Controllability ◽  
Bounded Input

<p style='text-indent:20px;'>The exact null-controllability problem in the class of smooth controls with applications to interconnected systems was considered in [<xref ref-type="bibr" rid="b23">23</xref>] for the case of bounded input operators appearing in systems with distributed controls. The current paper constitutes an extension of the [<xref ref-type="bibr" rid="b23">23</xref>] for the case of unbounded input operators (with more emphasis on the controllability of interconnected systems). The proofs of the results of [<xref ref-type="bibr" rid="b23">23</xref>] for the case of bounded input operators are adopted for the case of unbounded input operators.</p>

scholarly journals Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Sutrima Sutrima ◽  
Christiana Rini Indrati ◽  
Lina Aryati
Keyword(s):  
Control Systems ◽  
Approximate Controllability ◽  
Null Controllability ◽  
Control Problems ◽  
Output Stability ◽  
Sturm Liouville ◽  
Exact Null Controllability ◽  
Analysis Of Stability ◽  
The Stability ◽  
Controllability And Observability

In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated C0-quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability.

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