Ashyralyyev, Charyyar; Akkan, Pinar

We study a source identification problem for a parabolic equation with multipoint nonlocal boundary condition. Stability estimates for the solution of abstract source identification problem are established. In application, stability estimates for the solution of the overdetermined mixed boundary value problem for multidimensional parabolic equation are obtained. The first and second order of accuracy difference schemes for the approximate solution of this problem are constructed. Stability estimates for solutions of these difference schemes are proved. Numerical illustration for a simple test problem is presented.

Ashyralyyev, Charyyar

This paper addresses estimation of the solution of inverse problem for the elliptic type equation with second kind boundary conditions and Neumann-type overdetermination at the interior point. We prove various estimates for the solution of this identification problem. Then, the first order accuracy stable difference scheme is studied. The stability, almost coercive stability, and coercive stability inequalities for its solution are obtained. The theoretical results can be applied to investigate identification problems for multidimensional elliptic equation with different kind of boundary conditions.