Inverse Problem for a Parabolic Equation with Integral Condition

Abstract

This paper is devoted to study of the nonlocal inverse boundary-value problem for a second-order parabolic equation. First, we introduce a definition of a classical solution of the stated problem. Then, the initial problem is reduced to an equivalent problem, for which using the method of contraction mappings principle the theorem of the existence and uniqueness of solutions is proved. Moreover, using the equivalency, we prove the existence and uniqueness of classical solution of the original problem.