The inverse boundary spectral problem for a hyperbolic equation with first order perturbation

Abstract

We study an inverse boundary spectral problem for the hyperbolic equation in a bounded domain in . The corresponding time-harmonic equation can be written to a non-selfadjoint eigenvalue problem. We assume that the boundary spectral data, i.e., the eigenvalues and the boundary values of the generalized eigenfunctions of A are known. (This assumption is equivalent to that the singularities of the Neumann-to-Dirichlet mapping of the time-harmonic equation are known.) The main result is that the boundary spectral data determine a{x) uniquely and p(x) and q(x) within a generalized gauge transformation.

Keywords:

• Hyperbolic equations
• inverse inverse problems
• inverse boundary spectral problems

¹University of Helsinki, P. 0. Box 4(Yliopistonkatu S), RN-00014, Fin

¹University of Helsinki, P. 0. Box 4(Yliopistonkatu S), RN-00014, Fin

Notes

¹University of Helsinki, P. 0. Box 4(Yliopistonkatu S), RN-00014, Fin