Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics
Jorge Zubelli | Doumic Jauffret, Marie | Perthame, Benoit
Numerical Analysis; Analysis of PDEs; Quantitative Methods
We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We propose a new regularization technique based on a filtering approach. We prove convergence of the algorithm and validate the theoretical results by implementing numerical simulations, based on classical techniques. We compare the results for direct and inverse problems, for the filtering method and for the quasi-reversibility method proposed in [Perthame-Zubelli].