SOLVING TWO PARABOLIC INVERSE PROBLEMS WITH A NONLOCAL BOUNDARY CONDITION IN THE REPRODUCING KERNEL SPACE

Two inverse problems of determining an unknown source control parameter in a parabolic equation with a nonlocal boundary condition, and both integral and point overspecified conditions are investigated in a reproducing kernel space. The analytical solutions are represented in the form of a series. An iterative method is given for getting the approximate solutions. The convergence of the iterative method is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such inverse problems.