Identification of boundary conditions of a differential operator (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 = hindicated inhomogeneous equation, it is necessary to narrow the domain of definition of themaximum op erator. The narrowing usually o ccurs due to b oundary conditions. Thus, a class ofcorrect restrictions of the maximum op erator arises. In the second part of the article, we givethe 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 reconstructingtwo-point boundary value problems from a finite set of eigenvalues and give illustrative numericalexamples of approximate calculations of the coefficients of the boundary conditions. Note that theproblem 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 } .
Keywords: boundary conditions; correct narrowing