This paper investigates an inverse boundary-value problem with integral boundary condition for a second-order parabolic equation. The aim is to find the coefficient of time derivative of considered equation and prove existence and uniqueness of classical solution. For this, the equivalent relations between original and auxiliary non-self-adjoint boundary problems are constructed. Existence and uniqueness theorem for the solution of the equivalent problem is proved. Further, using the equivalency, the existence and uniqueness of classical solution for considered problem is studied.

inverse value problem, parabolic equation, classical solution, integral condition.