Search

In this paper, we investigate the viscoelastic wave equation with variable coefficients and a delay, which is subject to nonlinear and nonlocal boundary dissipation. The existence of strong and weak solutions is obtained by means of Faedo-Galerkin approximation and denseness argument. By introducing an equivalent energy functional and using the Riemannian geometry method, we show the general decay rate of energy when kernel function satisfies some sufficient small conditions that we provide the range accurately. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stabilization of Timoshenko systems with or without Kelvin–Voigt damping, in the presence of second sound. We have drawn conclusions that provide new insights into the effect of local Kelvin–Voigt damping. Our primary conclusion is that the exponential stability of the system achieved through local thermal damping will be destroyed by the local Kelvin–Voigt damping with a discontinuous coefficient at the interface. In particular, when local dissipation solely originates from the second sound, the system exhibits exponential stability. However, when Kelvin–Voigt damping is introduced into the local thermoelastic component, the system, surprisingly, loses its exponential stability. In this case, the corresponding solution decays polynomially with the rate t - 2 . [ABSTRACT FROM AUTHOR]

Uniform stabilization of a structural acoustic model describing an acoustic chamber with flexible curved wall is addressed. The coupled nonlinear system consists of a variable-coefficient wave equation and a shallow shell model which is used to model the flexible curved wall (interface). The coupling between the wave and the shell takes place on the interface. Derivation of stability estimates for the variable-coefficient coupled system with the shallow shell depends on the Riemannian geometry method and the multiplier technique. The uniform energy decay rates of the overall interactive model are achieved by introducing nonlinear boundary feedbacks applied to the wave equation and the shell model. [ABSTRACT FROM AUTHOR]

In this paper, the authors mainly consider the exact controllability for degenerate wave equation, which degenerates at the interior point, and boundary controls acting at only one of the boundary points. The main results are that, it is possible to control both the position and the velocity at every point of the body and at a certain time T for the wave equation with interior weakly degeneracy. Moreover, it is shown that the exact controllability fails for the wave equation with interior strongly degeneracy. In order to steer the system to a certain state, one needs controls to act on both boundary points for the wave equation with interior strongly degeneracy. The difficulties are addressed by means of spectral analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider stabilization of the transmission wave equation with variable coefficients, which has an acceleration term and interior delay. By using Riemannian geometry method and Lyapunov functional, we obtain the exponential decay for the solutions. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of the exact controllability for a system of weakly coupled one dimensional degenerate wave equations. An internal locally control acts on only one equation. We show that, when the coupling parameter which depends on the degree of degradation is sufficiently small, the observation of the velocity of the first component of the solution on a left neighborhood of x = 1 allow us to get back a weakened energy of initial data of the second component of the solution for a sufficiently large time T . Using the Hilbert Uniqueness Method, we then establish an indirect exact controllability result. [ABSTRACT FROM AUTHOR]

This paper studies the stability of Schrödinger equation with boundary control matched disturbance. The time-varying gain extended state observer is utilized to estimate disturbance and state. Meanwhile, the authors get a continuous controller by the active disturbance rejection control strategy, which shows that the closed-loop system of Schrödinger equation is asymptotically stable. These results are illustrated by simulation examples. [ABSTRACT FROM AUTHOR]

This paper studies the regularity of Euler-Bernoulli equations on a bounded domain of R ( n ≥ 2) with boundary controls and collocated observations. The authors consider the Dirichlet controls in the case of hinged and clamped boundary controls respectively. It is shown that the systemsare regular in the sense of G. Weiss. The feedthrough operators are founded to be zero. [ABSTRACT FROM AUTHOR]

The wave equation of variable coefficients in an exterior domain with a localized half-linear dissipation is considered. The energy decay estimate for the system is established by Riemannian geometry method. [ABSTRACT FROM AUTHOR]

This paper considers the stabilization of the transmission problem of wave equations with variable coefficients. By introducing both boundary feedback control and distribute feedback control near the transmission boundary, the author establishes the uniform energy decay rate for the problem. [ABSTRACT FROM AUTHOR]

We consider the exact controllability problem from boundary for thin shells. Under some checkable geometric assumptions on the middle surface, we establish the observability inequalities via the Bochner technique for the Dirichlet control and the Neumann control problems. We also give several examples to verify the geometric assumptions. [ABSTRACT FROM AUTHOR]