Inverse Source Problem for Heat Equation with Nonlocal Wentzell Boundary Condition

The inverse source problem for one-dimensional heat equation is investigated with nonlocal Wentzell–Neumann boundary and integral overdetermination conditions. The generalized Fourier method is used to show the existence, uniqueness and stability of the classical solution under some regularity, consistency and orthogonality conditions on the data. The considered inverse problem gives an idea of how total energy might be externally controlled.