Reconstruction of a convolution kernel in a semilinear parabolic problem   based on a global measurement
  A semilinear parabolic problem of second order with an unknown time-convolution kernel is considered. The missing kernel 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. 
R. H. De Staelen and M. Slodi\v{c}ka
math.AP