A half-inverse problem for the singular diffusion operator with jump conditions

TL;DR

This paper investigates a half-inverse spectral problem for a singular diffusion operator with jump conditions dependent on the spectral parameter, demonstrating how to recover coefficients and potentials from spectral data.

Contribution

It introduces a method to determine coefficients, potential functions, and jump condition parameters from spectral data for a diffusion operator with discontinuities.

Findings

Unique determination of potential functions from spectrum

Recovery of jump condition parameters from spectral data

Application of Hocstadt-Lieberman and Yang-Zettl methods

Abstract

In this paper, half inverse spectral problem for diffusion operator with jump conditions dependent on the spectral parameter and discontinuoty coeffcient is considered. The half inverse problems is studied of determining the coeffcient and two potential functions of the boundary value problem its spectrum by Hocstadt- Lieberman and Yang-Zettl methods. We show that two potential functions on the whole interval and the parameters in the boundary and jump conditions can be determined from spectrum.