Abstract:
Consider the problem of determining the coefficients in the differential equation of parabolic
types and boundary conditions on the known sections of the solutions of the initial-boundary
value problem. Used spectral approach based on spectral properties of the elliptic operator
of the initial-boundary value problem and the methods of solving the inverse spectral
problem of restoring the Sturm—Liouville operator on two sequences of the eigenvalues, that
corresponding to two sets of boundary conditions. In the work presented sufficient conditions
of determination of two sequences of the eigenvalues by two sets of boundary conditions and
terms of the uniqueness of the solution of the inverse problem The paper considers the case
where the initial-boundary value problem contains the specifics — the interval of change
contains variable include a finite number of the points, where the differential equation is
meaningless and replaced conditions agreement.
