共查询到20条相似文献，搜索用时 0 毫秒
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This paper deals with boundary exact controllability for the dynamics governed by the wave equation with variable coefficients in time and space, subject to Dirichlet or Neumann boundary controls. The observability inequalities are established by the Riemannian geometry method under some geometric conditions. 相似文献
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A model of the spacecraft control laboratory experiment with variable coefficients is considered. It is shown that the closed-loop system under boundary feedback damping has a sequence of generalized eigenfunctions, which form a Riesz basis for the state Hilbert space. The spectrum-determined growth condition, the exponential stability, and an asymptotic expression of the spectrum are obtained. Moreover, the exact controllability and exact observability of the system are also presented. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(7):2827-2847
In this paper, we consider the Bresse‐Cattaneo system with a frictional damping term and prove some optimal decay results for the L2‐norm of the solution and its higher order derivatives. In fact, we show that there is a completely new stability number δ that controls the decay rate of the solution. To prove our results, we use the energy method in the Fourier space to build some very delicate Lyapunov functionals that give the desired results. We also prove the optimality of the results by using the eigenvalues expansion method. In addition, we show that for the absence of the frictional damping term, the solution of our problem does not decay at all. This result improves some early results 相似文献
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In this work we consider the Bresse system with frictional damping operating only on the angle displacement and we show that under a certain assertion the solution decays polynomially and the decay rate is optimal. 相似文献
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Belkacem Said‐Houari Abdelaziz Soufyane 《Mathematical Methods in the Applied Sciences》2015,38(17):3642-3652
In this paper, we consider the Bresse system coupled with the Fourier law of heat conduction. We prove that the decay rate of the solution is very slow. In fact, we show that the L2‐norm of the solution decays with the rate of (1 + t)?1/12 similar to the one obtained for the Timoshenko system. In addition, we found that the wave speed of the first two equations still control the decay rate of the solution with respect to the regularity of the initial data. This seems to be the first result dealing with the behavior of the Cauchy problem in the Bresse–Fourier model. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Fatiha Alabau Boussouira Dilberto da S. Almeida Júnior 《Journal of Mathematical Analysis and Applications》2011,374(2):481-498
In this paper we study the Bresse system with frictional dissipation working only on the angle displacement. Our main result is to prove that this dissipative mechanism is enough to stabilize exponentially the whole system provided the velocities of waves propagations are the same. This result is significative only from the mathematical point of view since in practice the velocities of waves propagations are always different. In that direction we show that when the velocities are not the same, the system is not exponentially stable and we prove that the solution in this case goes to zero polynomially, with rates that can be improved by taking more regular initial data. Finally, we give some numerical result to verify our analytical results. 相似文献
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Maxim A. Medvedev T. E. Simos Ch. Tsitouras 《Mathematical Methods in the Applied Sciences》2019,42(2):710-716
A two–stage, explicit, hybrid four–step method of sixth order for the solution of the special second order initial value problem is presented here. The new method is trigonometric fitted, thus it uses variable coefficients. Numerical tests illustrate the superiority of our proposal over similar methods found in the relevant literature on a set of standard problems. 相似文献
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Maxim A. Medvedev T. E. Simos Ch. Tsitouras 《Mathematical Methods in the Applied Sciences》2019,42(6):2025-2032
A four‐step method of seventh algebraic order is presented. It is tuned for addressing the special second order initial value problem. The new method is hybrid, explicit, and uses three stages per step. In addition is phase fitted. In consequence it uses variable coefficients that depend on the magnitude of the step‐size. We also present numerical tests on a set of standard problems that illustrate the efficiency of the derived method over older ones given in the relevant literature. 相似文献
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M.O. Alves L.H. Fatori M.A. Jorge Silva R.N. Monteiro 《Mathematical Methods in the Applied Sciences》2015,38(5):898-908
This paper is concerned with asymptotic stability of a Bresse system with two frictional dissipations. Under mathematical condition of equal speed of wave propagation, we prove that the system is exponentially stable. Otherwise, we show that Bresse system is not exponentially stable. Then, in the latter case, by using a recent result in linear operator theory, we prove the solution decays polynomially to zero with optimal decay rate. Better rates of polynomial decay depending on the regularity of initial data are also achieved. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
10.
Kyungkeun Kang Seick Kim Aurelia Minut 《Journal of Mathematical Analysis and Applications》2004,299(1):89-99
The goal of this paper is to establish Hölder estimates for the solutions of a certain parabolic system related to Maxwell's equations arising in a quasi-stationary electromagnetic field. 相似文献
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In this paper, we consider the energy decay rate of a thermoelastic Bresse system with variable coefficients. Assume that the thermo-propagation in the system satisfies the Cattaneo's law, which can eliminate the paradox of infinite speed of thermal propagation in the assumption of the Fourier's law in the classical theory of thermoelasticity. Meanwhile, we also discuss the effect of a boundary viscoelastic damping on the stability of this system. By a detailed spectral analysis, we obtain the expressions of the spectrum and deduce some spectral properties of the system. Then based on the distribution of the spectrum, we prove that the energy of the system with a boundary viscoelastic damping decays exponentially. However, it no longer decays exponentially if there is no boundary damping. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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本利用相关的差分方程的全局吸引性研究了一类具时滞的非线性变系数差分方程ｘｎ＋１＝ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ１－ｃｘｎ－ｋ）的正平衡点ｘ＾－＝１的全局吸引性,获得了一个好的充分条件。 相似文献
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《Mathematische Nachrichten》2017,290(5-6):672-686
For a bounded sequence of matrices defining a nonautonomous dynamics with discrete time, we obtain all possible relations between the regularity coefficients introduced by Lyapunov, Perron and Grobman. This includes considering general inequalities between the coefficients and showing that these inequalities are the best possible, in the sense that for any three nonnegative numbers satisfying them, and for no others, there exists a bounded sequence of matrices having the numbers respectively as Lyapunov, Perron and Grobman coefficients. Moreover, we establish inequalities between the three coefficients and some other regularity coefficients. 相似文献
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In this paper, we consider a one‐dimensional linear Bresse system with infinite memories acting in the three equations of the system. We establish well‐posedness and asymptotic stability results for the system under some conditions imposed into the relaxation functions regardless to the speeds of wave propagations. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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介绍如何通过变换把二阶变系数线性微分方程转化为一阶非线性微分方程,进而利用待定系数法对其求解,并对二阶变系数线性微分方程与一阶常系数非线性微分方程的内在的关系进行讨论. 相似文献
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In this paper, the formats of Julia sets for a class of nonlinear complex dynamic systems with variable coefficients were studied under certain conditions. For the complex dynamic systems in piecewise cases, we proposed some methods to control the forms of their Julia sets and stable domains analytically. What’s more, we illustrated that our methods worked well by computational simulations. Our work provides a better understanding about how to control the Julia sets of certain complex dynamic systems. 相似文献
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一类非线性变系数差分方程正解的振动性 总被引：1，自引：0，他引：1
马满军 《纯粹数学与应用数学》2000,16(2):92-98
研究了一类具有时滞的非线笥变系数差分方程Ｘｎ＋１＝Ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ／１－ｃｘｎ－ｋ解的振动性,获得了其正解关于正平衡点ｘ＝１振动的好的充分条件。 相似文献