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Zeitschrift für Analysis und ihre Anwendungen

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Volume 17, Issue 1, 1998, pp. 67–87
DOI: 10.4171/ZAA/809

Published online: 1998-03-31

An Inverse Problem for a Viscoelastic Timoshenko Beam Model

Cecilia Cavaterra[1]

(1) 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 $w$ and of the mean angle of rotation $\varphi$. The damping mechanism is characterized by two time-dependent memory kernels, $a$ and $b$, which are a priori unknown. Provided that $(w, \varphi)$ 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 $(w, \varphi,a,b)$ on the data is shown.

Keywords: Inverse problems, viscoelasticity of integral type, Ttmoshenko beam

Cavaterra Cecilia: An Inverse Problem for a Viscoelastic Timoshenko Beam Model. Z. Anal. Anwend. 17 (1998), 67-87. doi: 10.4171/ZAA/809