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In this paper, we consider a vibrating system of Timoshenko-type in a bounded one-dimensional domain under Dirichlet–Dirichlet or Dirichlet–Neumann boundary conditions with one or two discrete time delays and one or two internal frictional dampings. First, we show that the system is well posed in the sens of semigroup theory. Second, we prove the exponential stability regardless to the speeds of wave propagation of the system if the weights of the time delays are smaller than the ones of the corresponding dampings, respectively. However, when the weight of one time delay is not smaller than the one of the corresponding damping, we prove the exponential stability in case of equal-speed wave propagation, and the polynomial stability in the opposite case. 相似文献
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Belkacem Said-Houari Salim. A. Messaoudi Aissa Guesmia 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(6):659-684
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in
both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain
class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends
on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and
Tatar (Appl. Anal. 87(3):247–263, 2008) and Liu (Nonlinear Anal. 71:2257–2267, 2009) in which only the exponential and polynomial decay rates are considered. 相似文献
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Boumedine Chentouf Aissa Guesmia 《Mathematical Methods in the Applied Sciences》2019,42(13):4584-4605
This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems. 相似文献
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The spontaneous magnetoresistance anisotropy has been measured for the ferromagnetic alloys PdNi, PdCo and PdFe. The results confirm the conclusion drawn from other data that in Pd, Ni and Co (but not Fe) possess local orbital moments. 相似文献
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Senoussi Guesmia 《Archiv der Mathematik》2013,101(3):293-299
In this note we consider a linear parabolic problem defined on a non-cylindrical unbounded domain Q. If Ω t denotes the section of Q above t, the Ω t size goes to +∞, when t → +∞, i.e. the sections Ω t become unbounded in some directions when the time t becomes large. Here a model problem is studied, but the technique used can be applied for a wide class of problems, as nonlinear ones, defined on more general domains Q as those introduced by Lions [11]. An asymptotically exponential convergence of the solutions of such problems towards the solution of an elliptic problem defined on a lower dimensional domain is established. 相似文献
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Aissa Guesmia Mokhtar Kirane 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(5):124
In this paper, we consider one-dimensional linear Bresse systems in a bounded open domain under Dirichlet–Neumann–Neumann boundary conditions with two infinite memories acting only on two equations. First, we establish the well-posedness in the sense of semigroup theory. Then, we prove two (uniform and weak) decay estimates depending on the speeds of wave propagations, the smoothness of initial data and the arbitrarily growth at infinity of the two relaxation functions. 相似文献
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Aissa Guesmia Salim A. Messaoudi 《Mathematical Methods in the Applied Sciences》2009,32(16):2102-2122
In this paper we consider the following Timoshenko system: with Dirichlet boundary conditions and initial data where a, b, g and h are specific functions and ρ1, ρ2, k1, k2 and L are given positive constants. We establish a general stability estimate using the multiplier method and some properties of convex functions. Without imposing any growth condition on h at the origin, we show that the energy of the system is bounded above by a quantity, depending on g and h, which tends to zero as time goes to infinity. Our estimate allows us to consider a large class of functions h with general growth at the origin. We use some examples (known in the case of wave equations and Maxwell system) to show how to derive from our general estimate the polynomial, exponential or logarithmic decay. The results of this paper improve and generalize some existing results in the literature and generate some interesting open problems. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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Senoussi Guesmia 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(5):2904-2921
Analyzing the viscoelastic problem for small vibrations of elastic strings, Kirchhoff and Carrier proposed two different models of nonlinear partial differential equations. By combining these two models, we deal here with some nonlocal hyperbolic problems that cover a large class of Kirchhoff and Carrier type problems. The existence of local solutions of degenerate problems as well as local and nonlocal solutions of nondegenerate problems is established. The proofs are based on the combination of the Schauder fixed point theorem with some asymptotic method. 相似文献