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Moore-Gibson-Thompson theory for thermoelastic dielectrics

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Applied Mathematics and Mechanics(English Edition) 2021年第2期42卷 309-316页

作者： J.R.FERNANDEZ R.QUINTANILLA Department of Applied Mathematics I University of VigoCampus As Lagoas MarcosendeVigo 36310Spain Department of Mathematics Polytechnic University of CataloniaTerrassa 08222Spain

We consider the system of equations determining the linear thermoelastic deformations of dielectrics within the recently called Moore-Gibson-Thompson(MGT)***,we obtain the system of equations for such a ***,we consider the case of a rigid solid and show the existence and the exponential decay of ***,we consider the thermoelastic case and obtain the existence and the stability of the *** decay of solutions in the one-dimensional case is also recalled.

关键词： Moore-Gibson-Thompson(MGT)thermoelastic dielectrics existence semigroup exponential decay

General decay of energy to a nonlinear viscoelastic two-dimensional beam

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Applied Mathematics and Mechanics(English Edition) 2018年第11期39卷 1661-1678页

作者： B.LEKDIM A.KHEMMOUDJ Faculty of Mathematics University of Sciences and Technology Houari Boumedienne

A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the pr... 详细信息

关键词： two-dimensional space viscoelastic beam nonlinear tension exponential decay Lyapunov functional

The coupling effect of air-bridges on broadband spiral inductors in SiC-based MMIC technology

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Chinese Physics B 2017年第8期26卷 529-535页

作者：郑佳欣马晓华卢阳赵博超张恒爽张濛陈丽香朱青郝跃 School of Advanced Material and Nanotechnology Xidian UniversityXi'an 710071China School of Microelectronics Xidian UniversityXi'an 710071China

The coupling effect of air-bridges on broadband spiral inductors in SiC-based MMIC technology has been investigated deeply. The fabricated 1-nH spiral inductor on SiC substrate demonstrates a self-resonant frequency of 51.6 GHz, with a peak Q-fact of 12.14 at 22.1 GHz. From the S-parameters measurements, the exponential decay phenomenon is observed for L, Q-factor, and SRF with the air-bridge height decreasing, and an analytic expression is concluded to exactly fit the measured data which can be used to predict the performance of the spiral inductor. All the coefficients in the formula have specific meaning. By means of establishing the lumped model, the parasitic coupling capacitance of the air-bridge has been extracted and presents the exponential decay with the air-bridge heights decreasing which indicates that this capacitor is directly related to the coupling effect of the air-bridge. Through the electromagnetic field distribution simulation, the details of the electric field around the air-bridge have been presented which demonstrate the formation and the variation principles of the coupling effect.

关键词： coupling effect air-bridge broadband spiral inductor exponential decay SiC MMIC

NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

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Chinese Annals of Mathematics,Series B 2003年第2期24卷 239-248页

作者： FENG SHAOJI FENG DEXING Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China. E-mail: fengshaoji0164@sina.comAcademy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China. E-mail: dxfeng@*** Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.

关键词： Wave equations Nonlinear boundary feedback exponential decay Asymptotic decay Riemannian manifold

THE exponential STABILIZATION FOR A SEMILINEAR WAVE EQUATION WITH LOCALLY DISTRIBUTED FEEDBACK

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Chinese Annals of Mathematics,Series B 2005年第3期26卷 323-334页

作者： JIACHAOHUA FENGDEXING InstituteofSystemsScience AcademyofMathematicsandSystemsScienceChineseAcademyofSciencesBeijing100080China／／GraduateSchooloftheChineseAcademyofSciencesBeijing100049China InstituteofSystemsScience AcademyofMathematicsandSystemsScienceChineseAcademyofSciencesBeijing100080China

This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that... 详细信息

关键词： Wave equations exponential decay Distributed damping Variable coefficients Riemannian manifold

Global solutions and blow-up for a class of strongly damped wave equations systems

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Frontiers of Mathematics in China 2022年第5期17卷 767-782页

作者： Yaojun YE Lanlan LI Department of Mathematics and Statistics Zhejiang University of Science and TechnologyHangzhou 310023China

The initial-boundary value problem for semilinear wave equation systems with a strong dissipative term in bounded domain is *** existence of global solutions for this problem is proved by using potential well method,and the exponential decay of global solutions is given through introducing an appropriate Lyapunov ***,blow-up of solutions in the unstable set is also obtained.

关键词： Nonlinear wave equations systems global solutions exponential decay blow-up

LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

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Acta Mathematica Scientia 2006年第1期26卷 163-178页

作者：贾月玲李海梁 LCP Institute of Applied Physics and Computational Mathematics Department of Mathematics Capital Normal University

A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.

关键词： Quantum hydrodynamic equation quantum Euler-Poisson system global existence of classical solution rlonlinear fourth-order wave equation exponential decay large-time behavior

Bresse Beam with Damping and Logarithmic Source

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Chinese Annals of Mathematics,Series B 2024年第5期45卷 685-702页

作者： Sebastiao CORDEIRO Carlos BALDEZ Carlos RAPOSO Ducival PEREIRA Octavio VERA Department of Mathematics Federal University of ParaAbaetetubaParaBrazil Department of Mathematics Federal University of ParaBragancaParaBrazil Department of Mathematics Federal University of ParaSalinopolisParaBrazil Department of Mathematics State University of ParaBelemParaBrazil Department of Mathematics University of TarapacaAricaChile

This paper investigates the stabilization of a Bresse system with internal damping and logarithmic *** authors use the potential well *** initial data in the stability set created by the Nehari surface,the existence of a global solution is proved by using Faedo-Galerkin's *** Nakao theorem gives the exponential decay.A numerical approach is presented to illustrate the results obtained.

关键词： Bresse beam Logarithmic source Global solution exponential decay Numerical approach

Large-Time Behavior of Periodic Solutions to Fractal Burgers Equation with Large Initial Data

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Chinese Annals of Mathematics,Series B 2012年第3期33卷 405-418页

作者： Lijuan WANG Weike WANG Department of Mathematics Shanghai Jiao Tong UniversityShanghai 200240China

The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily *** exponential decay estimates of the solutions are obtained for th... 详细信息

关键词： Fractal Burgers equation Large-time behavior Large initial data Periodic solution exponential decay