Exact null controllability of non-autonomous functional evolution systems with nonlocal conditions

2013 ◽  
Vol 33 (3) ◽  
pp. 747-757 ◽  
Author(s):  
Xianlong FU ◽  
Yu ZHANG
Keyword(s):  
Nonlocal Conditions ◽  
Null Controllability ◽  
Functional Evolution ◽  
Exact Null Controllability ◽  
Evolution Systems

scholarly journals On the finite approximate controllability for Hilfer fractional evolution systems with nonlocal conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 529-539
Author(s):  
Xianghu Liu
Keyword(s):  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Evolution System ◽  
Controlled Systems ◽  
Uniqueness Of The Solution ◽  
Fractional Evolution Systems ◽  
Evolution Systems

Abstract The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main results.

scholarly journals Null controllability of a nonlinear heat equation

2002 ◽  
Vol 7 (7) ◽  
pp. 375-383 ◽  
Author(s):  
G. Aniculăesei ◽  
S. Aniţa
Keyword(s):  
Heat Equation ◽  
Dirichlet Boundary ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Nonlinear Heat Equation ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Linearized System ◽  
Kakutani Fixed Point ◽  
Exact Null Controllability ◽  
Kakutani Fixed Point Theorem

We study the internal exact null controllability of a nonlinear heat equation with homogeneous Dirichlet boundary condition. The method used combines the Kakutani fixed-point theorem and the Carleman estimates for the backward adjoint linearized system. The result extends to the case of boundary control.

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>

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