On the Well-possedness of the Problem of Reconstruction of Non-separate Boundary Conditions

TL;DR

This paper investigates the uniqueness and reconstruction methods for a third-order differential inverse spectral problem with non-separated boundary conditions, providing theoretical results and practical algorithms.

Contribution

It establishes new theorems on the uniqueness of solutions and develops a method for reconstructing unknown boundary conditions using spectral data.

Findings

Proved two theorems on solution uniqueness

Developed a method to reconstruct boundary conditions from eigenvalues

Demonstrated the method with an example

Abstract

We consider an inverse spectral problem with the third-order differential equation and the non-separated boundary conditions. Two theorems on the uniqueness of the solution of this problem are proved, and a method for establishing the unknown conditions is obtained, using 19 eigenvalues. The method of approximate calculation of unknown boundary conditions is explained, with the help of an example.