The Application of Spectral Resolution of a Self-Adjoint Operator to Approximate Elliptic Source Identification Problem with Neumann-Type Integral Condition

The paper focuses on the study of an elliptic source identification problem (SIP) with an integral condition for derivatives. Absolute stable difference scheme (DS) is proposed. Stability inequalities for solution of DS are established. Primarily DS is converted to auxiliary difference problem with some non local condition. Uniqueness and existence solution of DS is achieved by applying spectral resolution of a self-adjoint operator. Later, obtained results are used to establish stability inequalities for solution of DS for Neumann-type elliptic multidimensional SIP with integral condition. Finally, numerical illustration for 2D test example is carried out.