Multidimensional inverse problems: uniqueness theorems

Uniqueness Theorems for Multidimensional inverse Problems with Unbounded Coefficients

Uniqueness Theorems for 30 Inverse Problems With Incomplete Data

In F&mm, Phys. Lett. 99A, (1983), 258-260, it is proved that a compactly supported inhomogeneity in the velocity profile is uniquely determined by the values of the acoustic pressure collected for aU positions of the source and receiver on the surface of the Earth (on the whole plane P) at low frequencies. Here it is proved that the data collected on Dr x Q2 sufl'ice for the uniqueness theorem ...

Uniqueness Theorems for Inverse Obstacle Scattering Problems in Lipschitz Domains

For the Neumann and Robin boundary conditions the uniqueness theorems for inverse obstacle scattering problems are proved in Lipschitz domains. The role of non-smoothness of the boundary is analyzed.

On the Uniqueness of Inverse Eigenvalue Problems

together with suitable boundary conditions is examined. It is shown that n + 1 spectra associated with n + 1 distinct sets of boundary conditions are required in order to reconstruct the unknown coefficients pl, . . . ,p , . The sixth order case is analogous to the eigenvalue problem for the spheroidal modes of vibrations of earth which have been used to infer the density, the bulk modulus and ...

The uniqueness theorem for inverse nodal problems with a chemical potential

In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.