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O. Yu. Imanuvilov, M. Yamamoto

Stability estimate in a Cauchy problem for a hyperbolic equation with variable coefficients

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.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 13, 11/2005
Seiten: 583 - 594

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