scholarly journals Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems

2020 ◽  
Vol 26 ◽  
pp. 117
Author(s):  
Tatsien Li ◽  
Bopeng Rao
Keyword(s):  
Complex System ◽  
Asymptotic Stability ◽  
Large Class ◽  
Elliptic Operators ◽  
Uniqueness Of Solution ◽  
Dissipative Systems ◽  
Rank Condition ◽  
Scalar Problem ◽  
Asymptotic Synchronization

We show that under Kalman’s rank condition on the coupling matrices, the uniqueness of solution to a complex system of elliptic operators can be reduced to the observability of a scalar problem. Based on this result, we establish the asymptotic stability and the asymptotic synchronization for a large class of linear dissipative systems.

Asymptotic synchronization of a coupled system of wave equations on a rectangular domain with reflecting sides

2021 ◽  
pp. 1-18
Author(s):  
Tatsien Li ◽  
Bopeng Rao
Keyword(s):  
Differential Operator ◽  
Wave Equations ◽  
Coupled System ◽  
Rectangular Domain ◽  
Uniqueness Of Solution ◽  
Rank Condition ◽  
Geometrical Condition ◽  
Asymptotic Synchronization

We show the sufficiency of Kalman’s rank condition for the uniqueness of solution to a coupled system of wave equations in a rectangular domain. The approach does not need any gap condition on the spectrum of the differential operator and the usual multiplier geometrical condition. Then, the study on the asymptotic synchronization by groups can be improved for the corresponding system.

scholarly journals Asymptotic stability of semigroups associated to linear weak dissipative systems

2004 ◽  
Vol 40 (3-4) ◽  
pp. 387-392 ◽  
Author(s):  
A.F. Pazoto ◽  
J.C. Vila Bravo ◽  
J.E. Muñoz Rivera
Keyword(s):  
Asymptotic Stability ◽  
Dissipative Systems

scholarly journals FREDHOLM AND PROPERNESS PROPERTIES OF QUASILINEAR ELLIPTIC SYSTEMS OF SECOND ORDER

2005 ◽  
Vol 48 (1) ◽  
pp. 91-124 ◽  
Author(s):  
Hicham G. Gebran ◽  
Charles A. Stuart
Keyword(s):  
Large Class ◽  
Unbounded Domains ◽  
Elliptic Systems ◽  
Single Equation ◽  
Elliptic Operators ◽  
Second Order ◽  
Subject Classification ◽  
Secondary 47A53 ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

AbstractFor a large class of subsets $\varOmega\subset\mathbb{R}^{N}$ (including unbounded domains), we discuss the Fredholm and properness properties of second-order quasilinear elliptic operators viewed as mappings from $W^{2,p}(\varOmega;\mathbb{R}^{m})$ to $L^{p}(\varOmega;\mathbb{R}^{m})$ with $N\ltp\lt\infty$ and $m\geq1$. These operators arise in the study of elliptic systems of $m$ equations on $\varOmega$. A study in the case of a single equation ($m=1$) on $\mathbb{R}^{N}$ was carried out by Rabier and Stuart.AMS 2000 Mathematics subject classification: Primary 35J45; 35J60. Secondary 47A53; 47F05

scholarly journals Asymptotic Stability and Asymptotic Synchronization of Memristive Regulatory-Type Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Jin-E Zhang
Keyword(s):  
Asymptotic Stability ◽  
Qualitative Analysis ◽  
Global Asymptotic Stability ◽  
General Class ◽  
Resistive Switch ◽  
Regulatory Type ◽  
Asymptotic Synchronization ◽  
Theoretical Results ◽  
Potential Successor ◽  
Global Asymptotic Synchronization

Memristive regulatory-type networks are recently emerging as a potential successor to traditional complementary resistive switch models. Qualitative analysis is useful in designing and synthesizing memristive regulatory-type networks. In this paper, we propose several succinct criteria to ensure global asymptotic stability and global asymptotic synchronization for a general class of memristive regulatory-type networks. The experimental simulations also show the performance of theoretical results.

scholarly journals Asymptotic Stability for Stochastic Dissipative Systems with a Hölder Noise

2019 ◽  
Vol 57 (4) ◽  
pp. 3046-3071 ◽  
Author(s):  
Luu Hoang Duc ◽  
Phan Thanh Hong ◽  
Nguyen Dinh Cong
Keyword(s):  
Asymptotic Stability ◽  
Dissipative Systems

A Reproducible Selective Stain for Cardiac Sarcoplasmic Reticulum

1974 ◽  
Vol 32 ◽  
pp. 214-215
Author(s):  
R. A. Waugh ◽  
J. R. Sommer
Keyword(s):  
Complex System ◽  
Electron Microscope ◽  
Sarcoplasmic Reticulum ◽  
Transmission Electron Microscope ◽  
Electron Microscopic ◽  
Cardiac Sarcoplasmic Reticulum ◽  
Transmission Electron

Cardiac sarcoplasmic reticulum (SR) is a complex system of intracellular tubules that, due to their small size and juxtaposition to such electron-dense structures as mitochondria and myofibrils, are often inconspicuous in conventionally prepared electron microscopic material. This study reports a method with which the SR is selectively “stained” which facilitates visualizationwith the transmission electron microscope.

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