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In this paper, we study the boundary stability of a linearly damped degenerate wave equation, and analyze the well-posedness of the system by means of semigroup theory. Then we show that the system can achieve exponential stability under a given boundary feedback condition by multiplier method and suitable estimation. [ABSTRACT FROM AUTHOR]

In this paper, we consider a semilinear wave equation with variable coefficients in a smooth domain, subject to acoustic boundary conditions and dissipative boundary memory feedback, where a general Borel measure is involved. We show that the decay rates of the energy associated to the semilinear systems are given implicitly as solutions of a first order nonlinear, dissipative ODE, which recovers and extends some of the results from the literature. To prove the main result we use energy multiplier methods, geometric analysis combined with Lasiecka and Tataru arguments. [ABSTRACT FROM AUTHOR]

We investigate the variable-coefficient wave equation with nonlinear acoustic boundary conditions and logarithmic nonlinearity source term. In addition, the damping is nonlinear, and plays a role only in part of the boundary. Using the semigroup theory, we state the existence and uniqueness of the local solutions. Accordingly, we prove that under some assumptions on the initial data, the local solution can be extended to be global. Particularly, it has been shown that the decay rates of the system are given implicitly as solutions to a first-order ODE by applying the Riemannian geometry method. [ABSTRACT FROM AUTHOR]

In this paper, we address exponential stabilization of transmission problem of the wave equation with linear dynamical feedback control. Using the classical energy method and multiplier technique, we prove that the energy of system exponentially decays. [ABSTRACT FROM AUTHOR]

In this paper, we consider stabilization of transmission of the wave equation with dynamical boundary conditions that include a delay term acts on the boundary. By introducing suitable energy function, we prove under some assumptions that the closed‐loop system is exponentially stable. In addition, we also consider the situation where the above system is controlled by distributed feedback near the transmission boundary and can also obtain exponential stability estimates with fewer assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we study one‐dimensional linear degenerate wave equations with a distributed controller. We establish observability inequalities for degenerate wave equation by multiplier method. We also deduce the exact controllability for degenerate wave equation by Hilbert uniqueness method when the control acts on the nondegenerate boundary. Moreover, an explicit expression for the controllability time is given. [ABSTRACT FROM AUTHOR]

In this paper, we consider exact control problem for a coupled system of plate with Gurtin‐Pipkin equation. Using duality arguments, the problem is reduced to the obtention of suitable observability estimates for the dual system. Firstly, we obtain the observability inequality of the dual system by means of multiplier method. Then, we prove that the system is exactly controllable based on the Hilbert Unique Method. [ABSTRACT FROM AUTHOR]

In this paper, we consider global nonexistence of a solution for coupled quasilinear system with damping and source under Dirichlet boundary condition. We obtain a global nonexistence result of solution by using the perturbed energy method, where the initial energy is assumed to be positive. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Two types of open-loop systems of an Euler-Bernoulli equation with variable coefficient and Dirichlet boundary control and collocated observation are considered. The uncontrolled boundary is either hinged or clamped. It is shown, with the help of multiplier method on Riemannian manifold, that in both cases, systems are well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. In addition, the feedthrough operators are found to be zero. The result implies that the exact controllability of open-loop is equivalent to the exponential stability of closed-loop under a proportional output feedback for these systems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We consider the stabilization of the shallow shell by boundary feedbacks where the model has a middle surface of any shape.First,we put the shallow shell model in a suitable semigroup scheme.The existence,the uniqueness,and the properties of solutions to the shallow shell are then treated by the semigroup approach and the regularity of elliptic boundary value problems.Finally, we establish the uniform energy decay rate for the shallow shell under some checkable geometric conditions on the middle surface. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a nonlinear viscoelastic wave equation with nonlinear boundary damping and source terms. Under some appropriate assumptions on the relaxation function and with certain initial data, the global existence of solutions and a general decay for the energy have been established. [Copyright &y& Elsevier]

Abstract: We consider the system of nonlinear wave equations with initial and Dirichlet boundary conditions. Under some suitable assumptions on the functions and , the initial data and the parameters in the equations, the theorems of global existence and nonexistence are proved. [Copyright &y& Elsevier]