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
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