共查询到19条相似文献,搜索用时 109 毫秒
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对一端固定,一端加剪切力反馈的Euler-Bernoulli梁,运用Legendre谱方法对一个非同位控制系统进行研究,得到了最优反馈增益系数和系统衰减率.结果表明这样的非同位控制系统可以有效的增大系统衰减率,使系统具有更好的稳定性.同时指出所研究的系统是极小相位的. 相似文献
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利用Dirac δ函数,在全域建立并求解集中阻尼弦的动力学方程,导出其本征方程组、频率方程和本征函数的一般形式,推导了单项阻尼下本征函数的具体形式,并分析了中点阻尼对本征解的影响.同时,讨论了混合动力学系统在频率 阻尼关系、衰减率和完全抑制振动的最优阻尼3个方面既不同于连续系统,又不同于离散系统的特性:1)系统频率与其阻尼无关;2)各阶本征函数在单位时间内的衰减率都相同,衰减率与本征值的阶次无关;3)当阻尼取2时,系统衰减率趋于无穷大,系统不能发生任何有阻尼振动. 相似文献
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梁振动边界反馈的最优反馈增益的数值解 总被引:2,自引:0,他引:2
本用Legendre谱方法估计一端固定,一端加弯矩耗散线性反馈的梁振动的闭环系统使能量最快衰减的最优反馈增益,我们给出了数值产生的图形结果,通过比较发现另一种非耗散的线性反馈在最优反馈增益下比相应的耗散线性反馈有更好的衰减率。 相似文献
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《纯粹数学与应用数学》2021,(3)
研究了一个具有三次非线性项的可积的两分量Camassa-Holm系统Cauchy问题解的持久性.通过用权函数估计的方法证明:如果两分量Camassa-Holm系统的初值以及初值的空间导数都以指数形式衰减,则两分量Camassa-Holm系统的强解也在无穷远处以指数形式衰减,进一步,给出了动量的最优衰减估计. 相似文献
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研究了一个具有三次非线性项的可积的两分量Camassa-Holm系统Cauchy问题解的持久性.通过用权函数估计的方法证明:如果两分量Camassa-Holm系统的初值以及初值的空间导数都以指数形式衰减,则两分量Camassa-Holm系统的强解也在无穷远处以指数形式衰减,进一步,给出了动量的最优衰减估计. 相似文献
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针对凸多乘积问题,提出一种求其全局最优解的近似算法.首先,通过引入参量获得一个等价问题,然后估计问题中每一乘积项的上下界,进而借助网格结点,获得一些凸规划问题,通过求解这些凸规划问题获得原问题的近似最优解.最后,给出了该算法的收敛性证明和计算复杂性分析. 相似文献
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Yanjin Wang 《Journal of Differential Equations》2013,254(5):2304-2340
We establish the time decay rates of the solution to the Cauchy problem for the two-species Vlasov–Poisson–Boltzmann system near Maxwellians via a refined pure energy method. The total density of two species of particles decays at the optimal algebraic rate as the Boltzmann equation, but the disparity between two species and the electric field decay at an exponential rate. This phenomenon reveals the essential difference when compared to the one-species Vlasov–Poisson–Boltzmann system or the Navier–Stokes–Poisson equations in which the electric field decays at the optimal algebraic rate, and compared to the Vlasov–Boltzmann system in which the disparity between two species decays at the optimal algebraic rate. Our achievement heavily relies on a reformulation of the problem which well displays the cancelation property of the two-species system, and our proof is based on a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis. 相似文献
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Luci Harue Fatori Rafael Prado da Silva 《Mathematical Methods in the Applied Sciences》2017,40(11):4211-4221
In this work, we analyze the existence, uniqueness, and asymptotic behavior of solution to the model of a thermoelastic mixture of type III. We establish sufficient conditions to guarantee the exponential decay of solutions. When the decay is not of exponential type, we prove that the solutions decay polynomially and we find the optimal polynomial decay rate. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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STABILIZATION OF VIBRATING BEAM BY VELOCITY FEEDBACK CONTROL 总被引:1,自引:0,他引:1
1IntroductionInrecentyearstherehasbeenmuchinterestintopicofcontrolandstabilizationofflexiblevibratingsystemdescribedbyaEuler-Bernoullibeamequationasfollowing(See[1]-[8]).Thequestionofstabilizationofsystem(1.O)hasbeenstudiedbymanyauthors.Forexample,seeLagnese[1],Chen.et.al[2],R.b.,b.,l3]forstabilization,Lagllese[5]forconcentratedS/A'sstabilization.Letusmentionthatthesepapersstudyasymptoticoruniformdecayforthecollsideredsystem,butnotprovetheoptimalityofthedecayrate.C..,.d[8]studytheoptimali… 相似文献
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Hans Engler 《Journal of Differential Equations》2002,185(1):348-369
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation of the traveling wave profile decays at an algebraic rate, then the solution is shown to converge to a shifted wave profile at a corresponding temporal algebraic rate, and optimal intermediate results that combine temporal and spatial decay are obtained. The proofs are based on a general interpolation principle which says that algebraic decay results of this form always follow if exponential temporal decay holds for perturbation with exponential spatial decay and the wave profile is stable for general perturbations. 相似文献
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John A. Morrison 《Queueing Systems》2010,66(4):351-367
We consider a system of three parallel queues with Poisson arrivals and exponentially distributed service requirements. The
service rate for the heavily loaded queue depends on which of the two underloaded queues are empty. We derive the lowest-order
asymptotic approximation to the joint stationary distribution of the queue lengths, in terms of a small parameter measuring
the closeness of the heavily loaded queue to instability. To this order the queue lengths are independent, and the underloaded
queues and the heavily loaded queue have geometrically and, after suitable scaling, exponentially distributed lengths, respectively.
The expression for the exponential decay rate for the heavily loaded queue involves the solution to an inhomogeneous linear
functional equation. Explicit results are obtained for this decay rate when the two underloaded queues have vastly different
arrival and service rates. 相似文献
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We consider homogeneous solutions of the Vlasov–Fokker–Planck equation in plasma theory proving that they reach the equilibrium with a time exponential rate in various norms. By Csiszar–Kullback inequality, strong L1-convergence is a consequence of the ‘sharp’ exponential decay of relative entropy and relative Fisher information. To prove exponential strong decay in Sobolev spaces Hk, k ⩾ 0, we take into account the smoothing effect of the Fokker–Planck kernel. Finally, we prove that in a metric for probability distributions recently introduced in [9] and studied in [4, 14] the decay towards equilibrium is exponential at a rate depending on the number of moments bounded initially. Uniform bounds on the solution in various norms are then combined, by interpolation inequalities, with the convergence in this weak metric, to recover the optimal rate of decay in Sobolev spaces. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons, Ltd. 相似文献
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In this article, we investigate a one-dimensional thermoelastic laminated beam system with nonlinear damping and viscoelastic dissipation on the effective rotation angle and through heat conduction in the interfacial slip equations. Under minimal conditions on the relaxation function and the relationship between the coefficients of the wave propagation speed of the first two equations, we show that the solution energy has an explicit and optimal decay rate from which the exponential and polynomial stability are just particular cases. Moreover, we establish a weaker decay result in the case of non-equal wave of speed propagation and give some examples illustrate our results. This work extends and improves the earlier results in the literature, particularly the result of Mukiawa et al. (2021). 相似文献
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In this work, we consider a coupled system of wave equations with memory only acting in one of the equations of the system. We show that the solution of this system has a polynomial rate of decay as time tends to infinity, but does not have exponential decay. 相似文献
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John A.D. Appleby David W. Reynolds 《Journal of Mathematical Analysis and Applications》2006,320(1):56-77
This paper considers the resolvent of a finite-dimensional linear convolution Volterra integral equation. The main results give conditions which ensure that the exact rate of decay of the resolvent can be determined using a positive weight function related to the kernel. The decay rates can be exponential or subexponential. Many other related results on exact rates of exponential and subexponential decay of solutions of Volterra integro-differential equations are given. We also present an application to a linear compartmental system with discrete and continuous lags. 相似文献