Determination of a solely time-dependent source in a semilinear parabolic problem by means of boundary measurements

A semilinear parabolic problem of second order with an unknown solely time-dependent source term is studied. The missing source is recovered from an additional integral measurement over the boundary. The global in time existence, uniqueness as well as the regularity of a solution are addressed. A new numerical scheme based on Rothe's method is designed and convergence of iterates towards the exact solution is shown.