A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping - Raposo, C. A.; Bastos, W. D.; Avila, J. A. J. (Natural Sciences Publishing Corporation, 2011)
In this work we consider a transmission problem for the longitudinal displacement of a Euler-Bernoulli beam, where one small part of the beam is made of a viscoelastic material with Kelvin-Voigt constitutive relation. We use semigroup theory to prove existence and uniqueness of solutions. We apply a general results due to L. Gearhart [5] and J. Pruss [10] in the study of asymptotic behavior of solutions and prove that the semigroup associated to the system is exponentially stable. A numerical scheme is presented,
Keywords: Transmission problem; Exponencial stability; Euler-Bernoulli beam; Kelvin-Voigt damping; Semigroup; Numerical scheme