On an Inverse Problem for a Parabolic Equation

In this paper, we study the inverse problem of the reconstruction of the right-hand side of special form for a parabolic equation in $u$ in which the coefficients of $u_t$ and $u$ depend on $u_(x,t)$ , with overdetermination given by the integral of the solution over time. The Fredholm property for this problem and the existence and uniqueness theorems in Sobolev spaces are established.