A Regularization Scheme for an Inverse Problem in Age-Structured Populations

AbstractThis paper considers the question of the stable determination of the death rate λ in the fundamental equation of age structured population dynamics ρt + ρa + λρ = 0. We assume that data consisting of population profiles at two distinct times are given. Our approach is to formulate the inverse problem as an operator equation and then, use a method of least squares for its solution. Since the problem is ill-posed, we have to consider a regularization technique. We prove that the resulting scheme has a convergence rate of Hölder type