Energy decay estimates for a wave equation with nonlinear boundary feedback

Abstract

Abstract. We study a wave equation in one dimensional space with nonlinear dissipative boundary feedback at both ends. We prove existence and uniqueness of solution, strong and uniform exponential decay of energy under some conditions in the nonlinear feedback. Decay rate estimates of the energy are given under weak growth assumptions on the feedback functions.

Numerical Approximation of Spectrum for Variable Coefficients Euler-Bernoulli Beams Under a Force Control in Position and Velocity

“…Finally, we study the influence of parameters α, β in velocity convergence of the system (3). The length of the beam is chosen to be unity, EI (x) = (1 + x) 4 , is the stiffness of the beam, and m (x) = (1 + x) 2 is the mass density.…”

“…In ( [4] and [10]) the authors proved that the fact of adding a control force in position to existing control in velocity, although preserving the Riesz basis NUMERICAL APPROXIMATION OF SPECTRUM FOR...…”

“…The idea of adding a control force in position to the existing feedback has been invoked by the studies of many authors (see [4]). …”