Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



An inverse problem for the linear viscoelastic Kirchhoff plate

Authors: Cecilia Cavaterra and Maurizio Grasselli
Journal: Quart. Appl. Math. 53 (1995), 9-33
MSC: Primary 73K10; Secondary 35R30, 45K05, 47N20, 73F15
DOI: https://doi.org/10.1090/qam/1315445
MathSciNet review: MR1315445
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Abstract: We consider the linear Kirchhoff plate model subject to a viscoelastic damping of integral type. The damping term contains a time-dependent convolution kernel accounting for the long-range memory effects. The mechanical behavior of the plate is influenced by this memory function which is a priori unknown. That leads us to consider the question of identifying it. We study this kind of inverse problem by using the integrodifferential evolution equation governing the vertical deflection of the plate and coupling it with a set of overposed initial and boundary conditions. The problem obtained is then reduced to a nonlinear Volterra integral equation of second kind for the unknown memory kernel. Then, via the Contraction Principle, we prove local (in time) existence and uniqueness results. In addition, we show the Lipschitz continuous dependence upon the data. These results also apply to a viscoelastic beam model.

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DOI: https://doi.org/10.1090/qam/1315445
Article copyright: © Copyright 1995 American Mathematical Society

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