An Inverse Problem for a Viscoelastic Timoshenko Beam Model

  • Cecilia Cavaterra

    Università degli Studi di Milano, Italy


We consider the Timoshenko model for a viscoelastic beam. This model consists in a system of two coupled Volterra integrodifferential equations describing the evolution of the mean displacement ww and of the mean angle of rotation φ\varphi. The damping mechanism is characterized by two time-dependent memory kernels, aa and bb, which are a priori unknown. Provided that (w,φ)(w, \varphi) solves a suitable initial and boundary value problem for the evolution system, the inverse problem of determining a and b fçom supplementary information is analyzed. A result of existence and uniqueness on a given bounded time interval is proved. In addition, Lipschitz continuous dependence of the solution (w,φ,a,b)(w, \varphi,a,b) on the data is shown.

Cite this article

Cecilia Cavaterra, An Inverse Problem for a Viscoelastic Timoshenko Beam Model. Z. Anal. Anwend. 17 (1998), no. 1, pp. 67–87

DOI 10.4171/ZAA/809