Mathematical Modeling of a Reaction-Diffusion System with a Free Boundary

Abstract

This article presents the application of a Stefan-type two-phase free boundary problem to model dynamics of the prosthesis-tissue interface in dentistry and prosthetics. Addressing
issues such as stress concentrations and tissue damage caused by biomechanical incompatibility,
a mathematical model based on reaction-diffusion equations is proposed to describe the temporal
evolution of the free boundary. The existence and uniqueness of global classical solution of the
model are rigorously proven. The regularity of the free boundary is examined, and a computational scheme is introduced to visualize the interface dynamics. The findings are directed towards
optimizing the long-term stability and osseointegration of dental prostheses.