On a mathematical model of tumor growth based on cancer stem cells
J. Ignacio Tello
We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution of different subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving boundary. The system includes non-local terms of integral type in the coefficients. Under some restrictions in the parameters we show that there exists a unique homogeneous steady state which is stable.
keywords: free boundary problems stability. Cancer steam cells
On a comparison method to reaction-diffusion systems and its applications to chemotaxis
Mihaela Negreanu J. Ignacio Tello
In this paper we consider a general system of reaction-diffusion equations and introduce a comparison method to obtain qualitative properties of its solutions. The comparison method is applied to study the stability of homogeneous steady states and the asymptotic behavior of the solutions of different systems with a chemotactic term. The theoretical results obtained are slightly modified to be applied to the problems where the systems are coupled in the differentiated terms and / or contain nonlocal terms. We obtain results concerning the global stability of the steady states by comparison with solutions of Ordinary Differential Equations.
keywords: asymptotic behavior sub- and super-solutions. Comparison method stability

Year of publication

Related Authors

Related Keywords

[Back to Top]