Identification of a memory kernel in a semilinear integrodifferential parabolic problem with applications in heat conduction with memory

In this contribution, the reconstruction of a solely time-dependent convolution kernel is studied in an inverse problem arising in the theory of heat conduction for materials with memory. The missing kernel is recovered from a measurement of the average of temperature. The existence, uniqueness and regularity of a weak solution is addressed. More specific, a new numerical algorithm based on Rothe's method is designed. The convergence of iterates to the exact solution is shown.