An Inverse Problem for a Parabolic Equation with Nonlocal Boundary Conditions and Two-point Overdetermination

Source abstract

This paper is devoted to the study of an inverse boundary value problem for a parabolic equation with nonlocal boundary conditions and two-point overdetermination. To analyze the solvability of the problem, we first consider the associated auxiliary inverse boundary value problem. Applying the Fourier method, the solution of the equivalent problem is reduced to a system of integral equations, and the existence and uniqueness of the solution to the auxiliary problem is proved using the contraction mapping principle in an appropriate functional space. Further, using the equivalence, the existence and uniqueness theorem for the classical solution of the original problem is proved.