Stability analysis for a peri-implant osseointegration model
This paper concerns the stability of the solution for a peri-implant osseointegration process. ``For certain parameter values, the solution has a `wave-like' profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This `wave-like' profile contradicts experimental observations.'' The authors investigate conditions, under which such profile appears in the solution and express them ``in terms of model parameters, by means of linear stability analysis, carried out at one of the constant solutions of the simplified system.'' The stability analysis is done for the reduced system of PDE's which is equivalent to the original system, with respect to the stability properties of constant solutions. The case of large perturbations is investigated as well. It has been shown that if the constant solution is unstable, then the solution of the system does not converge to it. Numerical tests are presented. They ``show, that stability of the constant solution could determine the behavior of the solution of the whole system, if certain initial conditions are considered.''
scientific article; zbMATH DE number 6133587