On determining a source function in a parabolic problem with the Cauchy data on a part of the lateral surface of a cylinder
We examine an inverse problem on determining a solution to a parabolic equation and an unknown right-hand side in this equation using the conventional conditions of the first or mixed initial-boundary problem supplemented with the Neumann data on a part of the lateral boundary of a cylinder. Under some conditions on the data, we prove the solvability of this problem in the Sobolev spaces.