Inverse Hyperbolic Problems with Time-Dependent Coefficients

By G. Eskin. 2005

83 citations recorded by the source corpus.

We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation. As a by-product we prove a similar result for the nonself-adjoint hyperbolic operator with time-independent coefficients.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b41eec503f3b4979798cf383f8143f4addb0351b

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In Computational Theory and Mathematics

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Citations in the corpus

Inverse problems for the connection Laplacian (2015, background): “3 are weakened, then all the known uniqueness results in the scalar case require additional assumptions on the global geometry of (M, g), see [14, 25, 28].”
Recent progress in the boundary control method (2007, methodology): “The same condition is used in the paper [62], where an approach incorporating some ideas of the BCm is proposed.”
The Calderón problem in transversally anisotropic geometries (2013, methodology): “However, in the end the simplicity assumption was used to produce solutions that concentrate near geodesics in (M0, g0) and also to show that the potentials can be determined by inverting the geodesic ray transform (actually with attenuation) in the transversal manifold.”