Dynamic Inverse Problem for a Hyperbolic Equation and Continuation of Boundary Data
نویسنده
چکیده
We consider an inverse problem for a second order hyperbolic initial boundary value problem on a compact Riemannian manifold M with boundary. Assume that we know ∂M and the Cauchy data on ∂M × [0, T ] of the solutions with vanishing initial data. In the paper we consider two problems. Firstly, when T is sufficiently large and the Riemannian manifold satisfies an additional geometrical condition, we show that we can continue the data on ∂M ×R+ without solving the inverse problem. Secondly, we show that it is possible to determine manifold M and the wave operator to within the group of the generalized gauge transformations.
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