We consider the problem of uniform stabilization of nonlinear hyperbolic equations, epitomized by the following three canonical dynamics: (1) the wave equation in the natural state space L2(Ω) × H(Ω), under nonlinear (and non-local) boundary dissipation in the Dirichlet B.C., as well as nonlinear internal damping; (2) a corresponding Kirchhoff equation in the natural state space [H(Ω) ∩H1 0 (Ω)...

We study the boundary controllability properties of a wave equation with structural damping ytt− yxx− 2ytxx = 0, y(0, t) = 0, y(1, t) = h(t) where 2 is a strictly positive parameter depending on the damping strength. We prove that this equation is not spectrally controllable and that the approximate controllability depends on the functional space in which the initial value Cauchy problem is stu...

An azimuthally symmetric radially sheared azimuthal flow is driven by a nondiffusive, or residual, turbulent stress localized to a narrow annular region at the boundary of a cylindrical magnetized helicon plasma device. A no-slip condition, imposed by ion-neutral flow damping outside the annular region, combined with a diffusive stress arising from turbulent and collisional viscous damping in t...

Damping is a critical design parameter for miniaturized mechanical resonators used in microelectromechanical systems (MEMS), nanoelectromechanical systems (NEMS), optomechanical systems, and atomic force microscopy for a large and diverse set of applications ranging from sensing, timing, and signal processing to precision measurements for fundamental studies of materials science and quantum mec...

We present the theory of damping of low-energy excitations of a trapped Bose condensate at finite temperatures, where the damping is provided by the interaction of these excitations with the thermal excitations. We emphasize the key role of stochastization in the behavior of the thermal excitations for damping in non-spherical traps. The damping rates of the lowest excita-tions, following from ...

We present the theory of damping of low-energy excitations of a trapped Bose condensate at finite temperatures, where the damping is provided by the interaction of these excitations with the thermal excitations. We emphasize the key role of stochastization in the behavior of the thermal excitations for damping in non-spherical traps. The damping rates of the lowest excita-tions, following from ...

In this paper, we study initial-boundary conditions for a coupled nonlinear wave equations with weak damping terms. The exponential growth for suf ciently large initial data is proved.

Abstract. We consider a model of the undamped shear beam with a destabilizing boundary condition. The motivation for this model comes from atomic force microscopy, where the tip of the cantilever beam is destabilized by van der Waals forces acting between the tip and the material surface. Previous research efforts relied on collocated actuation and sensing at the tip, exploiting the passivity p...