Résolution numérique de problèmes à frontière mobile issus de la biologie

Abstract

Moving boundary problems arise in various biological and industrial contexts, particularly in phase changes or the diffusion of substances like oxygen. These problems are complex due to the nonlinearities of partial differential equations and the additional challenge of determining the moving boundary itself. This thesis explores numerical and analytical solutions for these problems. A constrained integral method is used to model the temperature and interface position in phase change systems, as well as to describe oxygen diffusion in a spherical geometry with absorption. Third and sixth-degree polynomials provide an efficient approximate representation, and the results obtained align well with those from other numerical techniques. This work highlights the need for advanced tools to accurately model and solve these complex phenomena.