In a bounded domain Ω ⊂ , we consider a hyperbolic operator P with the principal term
− p(x,t)Δ. Under the assumption that the outer normal derivative of p is non-positive,
we will estimate u in U × (−t
0, t
0) by the Cauchy data on an open subset of ∂Ω × (−T, T), where t
0 < T is some constant and U is a neighbourhood of ∂Ω.
The condition on the normal derivative is physically understood and means that the wave speed does not decrease inward on ∂Ω.
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∗Department of Mathematics, Iowa State University, 400 Carver Hall, Ames IA 50011-2064, USA. E-mail: vika@iastate.edu
†Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914, Japan. E-mail: myama@ms.u-tokyo.ac.jp
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 13, Issue 6, Pages 583–594, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939405775199488,
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