Identification of boundary conditions of a differential operator - Kanguzhin, B. E.; Dairbayeva, G.; Madibaiuly, Zh. (Journal of Mathematics, Mechanics and Computer Science, 2019)
This pap er consists of three parts. To achieve uniqueness of the solution of the B max u = h indicated inhomogeneous equation, it is necessary to narrow the domain of definition of the maximum op erator. The narrowing usually o ccurs due to b oundary conditions. Thus, a class of correct restrictions of the maximum op erator arises. In the second part of the article, we give the pro of of Theorem 1 and the justification of the pro cedure for recovering b oundary functions σ 2 ( t ) , . . . , σ n ( t ) . In the third part of the article, we separately consider the case of reconstructing two-point boundary value problems from a finite set of eigenvalues and give illustrative numerical examples of approximate calculations of the coefficients of the boundary conditions. Note that the problem of recovering boundary functions σ 2 ( t ) , . . . , σ n ( t ) from the procedure we have proposed, the linear problem. This fact is not obvious if the initial set of boundary functions is restored σ j k .