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, 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.

Approximate Controllability Results for Linear Viscoelastic Flows

2016 ◽  
Vol 19 (3) ◽  
pp. 529-549 ◽  
Author(s):  
Shirshendu Chowdhury ◽  
Debanjana Mitra ◽  
Mythily Ramaswamy ◽  
Michael Renardy
Keyword(s):  
Approximate Controllability ◽  
Viscoelastic Flows ◽  
Linear Viscoelastic

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.

The Mechanism of Size-Based Particle Separation by Dielectrophoresis in the Viscoelastic Flows

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Teng Zhou ◽  
Yongbo Deng ◽  
Hongwei Zhao ◽  
Xianman Zhang ◽  
Liuyong Shi ◽  
...  
Keyword(s):  
Electric Field ◽  
Newtonian Fluid ◽  
Finite Size ◽  
Particle Separation ◽  
Weissenberg Number ◽  
Viscoelastic Flow ◽  
Viscoelastic Flows ◽  
Arbitrary Lagrangian Eulerian ◽  
Particle Movement ◽  
Physical Insight

Viscoelastic solution is encountered extensively in microfluidics. In this work, the particle movement of the viscoelastic flow in the contraction–expansion channel is demonstrated. The fluid is described by the Oldroyd-B model, and the particle is driven by dielectrophoretic (DEP) forces induced by the applied electric field. A time-dependent multiphysics numerical model with the thin electric double layer (EDL) assumption was developed, in which the Oldroyd-B viscoelastic fluid flow field, the electric field, and the movement of finite-size particles are solved simultaneously by an arbitrary Lagrangian–Eulerian (ALE) numerical method. By the numerically validated ALE method, the trajectories of particle with different sizes were obtained for the fluid with the Weissenberg number (Wi) of 1 and 0, which can be regarded as the Newtonian fluid. The trajectory in the Oldroyd-B flow with Wi = 1 is compared with that in the Newtonian fluid. Also, trajectories for different particles with different particle sizes moving in the flow with Wi = 1 are compared, which proves that the contraction–expansion channel can also be used for particle separation in the viscoelastic flow. The above results for this work provide the physical insight into the particle movement in the flow of viscous and elastic features.

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 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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