scholarly journals Exact Null Controllability of KdV-Burgers Equation with Memory Effect Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Rajagounder Ravi Kumar ◽  
Kil To Chong ◽  
Jong Ho Park
Keyword(s):  
Burgers Equation ◽  
Null Controllability ◽  
Carleman Estimates ◽  
External Control ◽  
Observability Inequality ◽  
Exact Null Controllability ◽  
Controllability Property ◽  
The Stability ◽  
With Memory

This paper is concerned with exact null controllability analysis of nonlinear KdV-Burgers equation with memory. The proposed approach relies upon regression tool to prove controllability property of linearized KdV-Burgers equation via Carleman estimates. The control is distributed along with subdomainω⊂Ωand the external control acts on the key role of observability inequality with memory. This description finally showed the exact null controllability guaranteeing the stability.

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.

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.

scholarly journals On a general degenerate/singular parabolic equation with a nonlocal space term

2021 ◽  
Author(s):  
Brahim Allal ◽  
Genni Fragnelli ◽  
Jawad Salhi
Keyword(s):  
Fixed Point ◽  
Parabolic Equation ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Heat Equations ◽  
Well Posedness ◽  
Nonlocal Problems ◽  
Singular Parabolic Equation ◽  
Controllability Property ◽  
T Tau

In this paper we study the null controllability for the problems associated to the operators y_t-Ay - \lambda/b(x) y+\int_0^1 K(t,x,\tau)y(t, \tau) d\tau, (t,x) \in (0,T)\times (0,1) where Ay := ay_{xx} or Ay := (ay_x)_x and the functions a and b degenerate at an interior point x0 Ë .0; 1/. To this aim, as a first step we study the well posedness, the Carleman estimates and the null controllability for the associated nonhomogeneous degenerate and singular heat equations. Then,using the Kakutani’s fixed point Theorem, we deduce the null controllability property for the initial nonlocal problems.

scholarly journals On the influence of memory on complex dynamics of evolutionary oligopoly models

2020 ◽  
Vol 102 (2) ◽  
pp. 1097-1110 ◽  
Author(s):  
Gian Italo Bischi ◽  
Fabio Lamantia ◽  
Bruno Scardamaglia
Keyword(s):  
Local Stability ◽  
Nash Equilibria ◽  
Complex Dynamics ◽  
Model Complexity ◽  
Global Dynamics ◽  
Behavioral Rules ◽  
The Stability ◽  
Generic Strategies ◽  
With Memory

AbstractIn this paper, we propose a unitary formulation for evolutionary oligopoly models with memory. In particular, we consider behavioral rules that are stationary at the Nash equilibria so that we can study the stability of the oligopolistic model with memory with generic strategies for determining quantities. Although the introduction of memory does not affect the local stability properties of equilibria, we show how the presence of memory impacts the global dynamics of the system and how the question about the role of memory does not always provide a clear answer in terms of model complexity.

A Statistical Study of Process Variables to Optimize a High Speed Curtain Coater: Part I

TAPPI Journal ◽  
2009 ◽  
Vol 8 (1) ◽  
pp. 20-26 ◽  
Author(s):  
PEEYUSH TRIPATHI ◽  
MARGARET JOYCE ◽  
PAUL D. FLEMING ◽  
MASAHIRO SUGIHARA
Keyword(s):  
Boundary Layer ◽  
Experimental Design ◽  
High Speed ◽  
Statistical Study ◽  
Process Variables ◽  
High Speeds ◽  
The Stability ◽  
Air Removal ◽  
Removal System

Using an experimental design approach, researchers altered process parameters and material prop-erties to stabilize the curtain of a pilot curtain coater at high speeds. Part I of this paper identifies the four significant variables that influence curtain stability. The boundary layer air removal system was critical to the stability of the curtain and base sheet roughness was found to be very important. A shear thinning coating rheology and higher curtain heights improved the curtain stability at high speeds. The sizing of the base sheet affected coverage and cur-tain stability because of its effect on base sheet wettability. The role of surfactant was inconclusive. Part II of this paper will report on further optimization of curtain stability with these four variables using a D-optimal partial-facto-rial design.

The Role of Hydrophobicity in the Stability and pH-Switchability of (RXDX)4 and Coumarin-RXDX Conjugate β-Sheets

2020 ◽  
Author(s):  
Ryan Weber ◽  
Martin McCullagh
Keyword(s):  
Biological Imaging ◽  
Ph Sensing ◽  
Hydrophobic Residue ◽  
Ideal Candidate ◽  
Self Assembling ◽  
Sensing Applications ◽  
Β Sheets ◽  
The Stability ◽  
Dynamics Simulations

<p>pH-switchable, self-assembling materials are of interest in biological imaging and sensing applications. Here we propose that combining the pH-switchability of RXDX (X=Ala, Val, Leu, Ile, Phe) peptides and the optical properties of coumarin creates an ideal candidate for these materials. This suggestion is tested with a thorough set of all-atom molecular dynamics simulations. We first investigate the dependence of pH-switchabiliy on the identity of the hydrophobic residue, X, in the bare (RXDX)<sub>4</sub> systems. Increasing the hydrophobicity stabilizes the fiber which, in turn, reduces the pH-switchabilty of the system. This behavior is found to be somewhat transferable to systems in which a single hydrophobic residue is replaced with a coumarin containing amino acid. In this case, conjugates with X=Ala are found to be unstable and both pHs while conjugates with X=Val, Leu, Ile and Phe are found to form stable β-sheets at least at neutral pH. The (RFDF)<sub>4</sub>-coumarin conjugate is found to have the largest relative entropy value of 0.884 +/- 0.001 between neutral and acidic coumarin ordering distributions. Thus, we posit that coumarin-(RFDF)<sub>4</sub> containing peptide sequences are ideal candidates for pH-sensing bioelectronic materials.</p>

Metal-Metal Cooperative Bond Activation by Heterobimetallic Alkyl, Aryl, and Acetylide PtII/CuI Complexes

2020 ◽  
Author(s):  
Shubham Deolka ◽  
Orestes Rivada Wheelaghan ◽  
Sandra Aristizábal ◽  
Robert Fayzullin ◽  
Shrinwantu Pal ◽  
...  
Keyword(s):  
Alkyl Group ◽  
Bond Activation ◽  
Bond Cleavage ◽  
Terminal Alkyne ◽  
Alkyl Aryl ◽  
Metal Metal ◽  
The Stability ◽  
Selective Formation ◽  
Organoplatinum Compounds

We report selective formation of heterobimetallic PtII/CuI complexes that demonstrate how facile bond activation processes can be achieved by altering reactivity of common organoplatinum compounds through their interaction with another metal center. The interaction of the Cu center with Pt center and with a Pt-bound alkyl group increases the stability of PtMe2 towards undesired rollover cyclometalation. The presence of the CuI center also enables facile transmetalation from electron-deficient tetraarylborate [B(ArF)4]- anion and mild C-H bond cleavage of a terminal alkyne, which was not observed in the absence of an electrophilic Cu center. The DFT study indicates that the role of Cu center acts as a binding site for alkyne substrate, while activating its terminal C-H bond.

LANDSLIDE RISK MANAGEMENT IN THE COASTAL ZONE OF THE KUIBYSHEV RESERVOIR DUE THE DESIGN OF HIGH-SPEED LINE "MOSCOW-KAZAN"

2017 ◽  
Author(s):  
Nikolai Petrov ◽  
Nikolai Petrov ◽  
Inna Nikonorova ◽  
Inna Nikonorova ◽  
Vladimir Mashin ◽  
...  
Keyword(s):  
High Speed ◽  
Computational Models ◽  
Stable State ◽  
Landslide Risk ◽  
Kuibyshev Reservoir ◽  
Stepped Surface ◽  
The Stability ◽  
Landslide Slope ◽  
The Village

High-speed railway "Moscow-Kazan" by the draft crosses the Volga (Kuibyshev reservoir) in Chuvashia region 500 m below the village of New Kushnikovo. The crossing plot is a right-bank landslide slope with a stepped surface. Its height is 80 m; the slope steepness -15-16o. The authors should assess the risk of landslides and recommend anti-landslide measures to ensure the safety of the future bridge. For this landslide factors have been analyzed, slope stability assessment has been performed and recommendations have been suggested. The role of the following factors have been analyzed: 1) hydrologic - erosion and abrasion reservoir and runoff role; 2) lithologyc (the presence of Urzhum and Northern Dvina horizons of plastically deformable rocks, displacement areas); 3) hydrogeological (the role of perched, ground and interstratal water); 4) geomorphological (presence of the elemental composition of sliding systems and their structure in the relief); 5) exogeodynamic (cycles and stages of landslide systems development, mechanisms and relationship between landslide tiers of different generations and blocks contained in tiers). As a result 6-7 computational models at each of the three engineering-geological sections were made. The stability was evaluated by the method “of the leaning slope”. It is proved that the slope is in a very stable state and requires the following measures: 1) unloading (truncation) of active heads blocks of landslide tiers) and the edge of the plateau, 2) regulation of the surface and groundwater flow, 3) concrete dam, if necessary.

Short-Term Ultramicronized Palmitoylethanolamide Therapy in Patients with Myasthenia Gravis: a Pilot Study to Possible Future Implications of Treatment

2019 ◽  
Vol 18 (3) ◽  
pp. 232-238 ◽  
Author(s):  
Emanuela Onesti ◽  
Vittorio Frasca ◽  
Marco Ceccanti ◽  
Giorgio Tartaglia ◽  
Maria Cristina Gori ◽  
...  
Keyword(s):  
Pilot Study ◽  
Myasthenia Gravis ◽  
Repetitive Nerve Stimulation ◽  
Beneficial Effects ◽  
Antibody Titers ◽  
The Stability ◽  
Ultramicronized Palmitoylethanolamide ◽  
Open Pilot

Background: The cannabinoid system may be involved in the humoral mechanisms at the neuromuscular junction. Ultramicronized-palmitoylethanolamide (μm-PEA) has recently been shown to reduce the desensitization of Acetylcholine (ACh)-evoked currents in denervated patients modifying the stability of ACh receptor (AChR) function. <p> Objective: To analyze the possible beneficial effects of μm-PEA in patients with myasthenia gravis (MG) on muscular fatigue and neurophysiological changes. <p> Method: The duration of this open pilot study, which included an intra-individual control, was three weeks. Each patient was assigned to a 1-week treatment period with μm-PEA 600 mg twice a day. A neurophysiological examination based on repetitive nerve stimulation (RNS) of the masseteric and the axillary nerves was performed, and the quantitative MG (QMG) score was calculated in 22 MG patients every week in a three-week follow-up period. AChR antibody titer was investigated to analyze a possible immunomodulatory effect of PEA in MG patients. <p> Results: PEA had a significant effect on the QMG score (p=0.03418) and on RNS of the masseteric nerve (p=0.01763), thus indicating that PEA reduces the level of disability and decremental muscle response. Antibody titers did not change significantly after treatment. <p> Conclusion: According to our observations, μm-PEA as an add-on therapy could improve muscular response to fatigue in MG. The possible modulation of AChR currents as a means of eliciting a direct effect from PEA on the conformation of ACh receptors should be investigated. The co-role of cytokines also warrants an analysis. Given the rapidity and reversibility of the response, we suppose that PEA acts directly on AChR, though further studies are needed to confirm this hypothesis.

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