Uniform Stabilization of the wave equation on compact surfaces and locally distributed damping
M. M. Cavalcanti, V. N. Domingos Cavalcanti, R. Fukuoka, J. A. Soriano
本文研究了具有局部分布阻尼的紧致曲面上的波动方程。我们研究的情况下，阻尼是有效的补充可见脐带套。
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective on the complement of visible umbilical sets.
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In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using frequency domain approach combining with multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling …
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研究一类由（双曲）偏微分方程描述的弹性系统。我们的工作例子是一个振动的弦受到线性扰动的方程。主要目标是建立稳定和渐近稳定的条件，通过应用快速振荡控制的字符串。在第一种情况下，我们假设系统受到阻尼力的影响，接下来我们考虑没有阻尼的系统。我们扩展了高阶平均和时间演算的工具，用于研究这种分布参数系统的稳定性。
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本文研究了具有局部分布阻尼的紧致曲面上的波动方程。我们研究的情况下，阻尼是有效的，在一个精心挑选的子集的任意小的措施。
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We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's invariance principle we show that the energy of the system is Strongly stable. Then, based on a resolvent approach we show a luck of uniform stabilization. Next, using multiplier techniques combined with the frequency domain method, we shall give a polynomially stabilization result under some consideration on the stabilization of an auxiliary dissipating syste…
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Strict Lyapunov function for the one-dimensional linear wave equation with a locally distributed damping
针对带局部分布阻尼和狄利克雷边界条件的一维线性波动方程，构造显式严格李雅普诺夫函数。
Stabilization for degenerate equations with drift and small singular term
研究带漂移和非散度形式主导算子的一维退化/奇异波动方程，在退化端施加齐次Dirichlet条件、另一端施加边界阻尼，给出解的指数一致衰减条件。
In this paper, we investigate the stabilization of a linear Bresse system with one discontinuous local internal viscoelastic damping of Kelvin-Voigt type acting on the axial force, under fully Dirichlet boundary conditions. First, using a general criteria of Arendt-Batty, we prove the strong stability of our system. Finally, using a frequency domain approach combined with the multiplier method, we prove that the energy of our system decays polynomially with different rates.
Stabilization of the Gear-Grimshaw system on a periodic domain
本文研究了周期区域上两个Korteweg-de Vries方程在内部阻尼项作用下的非线性耦合系统的解。Gear和Grimshaw介绍了该系统，以模拟分层流体中二维长重力内波传播的相互作用。通过设计一个时变反馈控制律，利用李雅普诺夫方法，我们在任意正整数阶的索伯列夫空间中建立了解的指数稳定性。
In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region satisfy some geometric conditions, under the equality speed propagation and the coupling parameter of the two equations is small enough, we show the strong stability of our system in the absence of the compactness of the resolvent. Our system is not uniformly stable in general since it is the case of the interval. Hence, we look for a polynomial decay rate for sm…
Well-posedness and stabilization of a model system for long waves posed on a quarter plane
本文研究了两个KdV方程组的耦合系统在正射线上的一个初边值问题，该系统具有局部阻尼项.该模型出现时，建模由造波机在一个通道中产生的长波的传播。结果表明，该系统的解是指数稳定的，在加权空间$L^2(e^{2bx}dx)$中的$b>0$的整体适定性。利用李雅普诺夫方法研究了系统的镇定问题，并结合不动点参数和能量型估计得到了系统的适定性结果.
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