Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions

This paper investigates the inverse problem of finding a time-dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method. Numerical tests using the Crank–Nicolson finite difference scheme combined with an iterative method are presented and discussed.