Stability of an abstract-wave equation with delay and a Kelvin–Voigt damping

Stability of an abstract-wave equation with delay and a Kelvin-Voigt damping

Local Existence And Stability Results For A Wave Equation With Damping On All R

We discuss the local existence results of the solutions for the nonlocal hyperbolic problem 2 ( ) || ( ) || ( ) 0, tt t u x u t u u        , N x R  0, t  with initial conditions 0 ( ,0) ( ) u x u x  and 1 ( ,0) ( ), t u x u x  in the case where 3, 0 N    and 1 ( ( )) ( ) x g x    is a positive function lying in / ( ) ( ). N N N L R L R  When the initial energy 0 1 ( , ) E u u...

A Wave Equation with Discontinuous Time Delay

The influence of certain discontinuous delays on the behavior of the solutions of the wave equation is studied.

On the Controllability of a Wave Equation with Structural Damping

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...

Asymptotic Stability of the Wave Equation on Compact Surfaces and Locally Distributed Damping - a Sharp Result

This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping, described by utt −∆Mu+ a(x) g(ut) = 0 on M× ]0,∞[ , where M ⊂ R is a smooth oriented embedded compact surface without boundary. Denoting by g the Riemannian metric induced on M by R, we prove that for each ǫ > 0, there exist an open subset V ⊂ M and a smooth function f : M → R such t...