Resumen de Error analysis in the reconstruction of a convolution kernel in a semilinear parabolic problem with integral overdetermination

R.H. De Staelen, K. Van Bockstal, Marián Slodicka

• A semilinear parabolic problem of second order with an unknown solely time-dependent convolution kernel is considered. An additional given global measurement (a space integral of the solution) ensures the existence of a unique weak solution. The unknown kernel function can be approximated by a time-discrete numerical scheme based on Backward Euler�s method (Rothe�s method). In this contribution, an error analysis for the time discretization is performed of the existing numerical algorithm. Numerical experiments support the theoretically obtained results.