Numerical solution of an inverse problem in size-structured population dynamics

Abstract

We consider a size-structured model for cell division and address the\nquestion of determining the division (birth) rate from the measured stable size\ndistribution of the population. We propose a new regularization technique based\non a filtering approach. We prove convergence of the algorithm and validate the\ntheoretical results by implementing numerical simulations, based on classical\ntechniques. We compare the results for direct and inverse problems, for the\nfiltering method and for the quasi-reversibility method proposed in\n[Perthame-Zubelli].\n