An inverse source problem in a semilinear time-fractional diffusion equation

We study an inverse source problem for a semilinear time-fractional diffusion equation of second order in a bounded domain in Rd. The missing solely time-dependent source is recovered from an additional integral measurement. The existence, uniqueness and regularity of a weak solution is addressed. We design a numerical algorithm based on Rothe's method, derive a priori estimates and prove convergence of iterates towards the exact solution. Theoretical results are supported by a numerical experiment.