DISJOINT DATA INVERSE PROBLEM ON MANIFOLDS WITH QUANTUM CHAOS BOUNDS
Lassas M. Nursultanov M. Oksanen L. Ylinen L.
2024Society for Industrial and Applied Mathematics Publications
SIAM Journal on Mathematical Analysis
2024#56Issue 67748 - 7779 pp.
We consider the inverse problem to determine a smooth compact Riemannian manifold (M, g) from a restriction of the source-to-solution operator, ΛS,R for the wave equation on the manifold. Here, S and R are open sets on M, and ΛS,R represents the measurements of waves produced by smooth sources supported on S and observed on R . We emphasize that S and R could be disjoint. We demonstrate that ΛS,R determines the manifold (M, g) uniquely under the following spectral bound condition for the set S : There exists a constant C > 0 such that any normalized eigenfunction φ of the Laplace-Beltrami operator on (M, g) satisfies 1 ≤ C|| φ | S | L2(S). We note that, for the Anosov surface, this spectral bound condition is fulfilled for any nonempty open subset S. Moreover, we solve the analogue of this problem for the heat equation by showing that the source-to-solution maps for the heat and wave equations determine each other. Copyright
disjoint data , inverse problems , quantum chaos , Riemannian wave equation , source-to-solution map
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Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Electronics and Nanoengineering, Aalto University, Aalto, Finland
Department of Mathematics and Statistics
Department of Mathematics and Statistics
Institute of Mathematics and Mathematical Modeling
Department of Electronics and Nanoengineering
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