Electron. J. Differential Equations, Vol. 2019 (2019), No. 31, pp. 1-16.

Reachability of a second-order integro-differential equation on Riemannian manifold for a viscoelasticity model

Kang Zhou

Abstract:
We study a reachability problem for a second-order integro-differential equation on a finite-dimensional Riemannian manifold, which is a model equation for viscoelasiticity. We apply a Carleman estimate for the wave equations on Riemannian manifolds to establish the observability inequality.

Submitted April 11, 2018. Published February 20, 2019.
Math Subject Classifications: 93B05, 93B27, 35L10, 58J45.
Key Words: Reachability; integro-differential equation; Carleman estimates; Riemannian wave.

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Kang Zhou
Key Laboratory of Systems and Control
Institute of Systems Science
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing 100190, China
email: zhoukang14@mails.ucas.ac.cn

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