In this paper, we consider the numerical approximation of Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering is for an inhomogeneous isotropic medium. These eigenvalues have been proposed to be used as a target signature since they can recovered from data. A Galerkin method studied where basis functions are Neumann eigenfunctions Laplacian. Error es...

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

17.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 17.2THE INVERSE HEAT-CONDUCTION PROBLEM A SPECTRAL STOCHASTIC APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 17.2.1Introduction: Representation of random variables . . . . . . . . . . . 9 17.2.2The stochastic inverse heat-conduction problem (SIHCP): Problem definition ....

Motivated by the study of certain nonlinear wave equations (in particular, the Camassa–Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form −u′′ = z uω + zuυ on an interval [0, L), where ω is a real-valued distribution in H−1 loc [0, L), υ is a non-negative Borel measure on [0, L) and z is a complex spectral parameter. Apa...

In these five lectures1 on the spectral, and more particularly the inverse spectral theory of the Dirichlet problem in planar domains I wish to show how the investigation of a concrete mathematical question can draw on quite extensive areas of mathematics. Thus I hope that these talks will help to bind together various parts of the material you will have seen, or be seeing, elsewhere in this Wo...