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We study the energy decay for a variable-coefficient wave equation with memory type acoustic boundary conditions. Boundary memory is described by an integral term. Applying the Riemannian geometry method, we obtain the uniform energy decay under some conditions on the memory function and the coefficient matrix. [ABSTRACT FROM AUTHOR]

Abstract: Under appropriate assumptions the higher order energy decay rates for the damped wave equations with variable coefficients in are established. The results concern weighted (in time) and pointwise (in time) energy decay estimates. We also obtain weighted estimates for spatial derivatives. [Copyright &y& Elsevier]

Abstract: In this work, we are concerned with the boundary stabilization of a one-dimensional anti-stable wave equation corrupted by a boundary disturbance. We firstly propose, by weighed moving average technique, a state observer to make an estimation of the disturbance. Secondly, we design a control by the active disturbance rejection strategy to stabilize the system. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the following problem where is a bounded open interval in , and . We are interested in the interaction between the boundary damping and the interior source . Under some appropriate assumptions on the initial data, two blow-up results with positive initial energy are established. Furthermore, we obtain that the solutions blow up if p or is sufficiently large. [Copyright &y& Elsevier]

This paper deals with a Cauchy problem for the elasticity system with a structural damping. The decay rates of the total energy of the system are presented by applying the Fourier transform and multiplier in the Fourier space. Furthermore, almost optimal decay estimates of the total energy are obtained based on the Haraux–Komornik inequality. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the following reaction diffusion model, where D is a bounded domain in with smooth boundary ∂D, . This paper deals with interactions among three kinds of nonlinear mechanisms: nonlinear reaction, nonlinear convection and nonlinear boundary flux. The existence theorems of blow-up positive solutions, upper bound of “blow-up time,” upper estimates of “blow-up rate,” existence theorems of global positive solutions, and upper estimates of global positive solutions are given under suitable assumptions on and initial data . [Copyright &y& Elsevier]