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 and of the mean angle of rotation . The damping mechanism is characterized by two time-dependent memory kernels, and , which are a priori unknown. Provided that 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 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. 67–87DOI 10.4171/ZAA/809