Preprint 2025-07
Aníbal Coronel, Fernando Huancas, Mauricio Sepúlveda:
Theoretical and numerical approaches of reaction term identification in a SIS reaction diffusion system
Abstract:
We introduce the necessary conditions for existence and uniqueness of coefficients determination problem in a class of reaction-diffusion systems from a knowledge of an approximation of the state variables at the end of the processes. The system considered is a generalization of the susceptible-infected-susceptible (SIS) model disease transmission under the assumption of diffusion. We introduce a formulation of the inverse problem as a constrained optimization problem for an appropriate cost functional. In the main results of the paper, we prove the existence of a minimizer for the cost functional, introduce a first order necessary optimality condition, deduce stability of the inverse problem unknowns with respect to the observations, and demonstrate the uniqueness up an additive constant of identification problem. In addition, we introduce a numerical approach of the inverse problem in the case of parameter identification problem and consider a numerical example.
