Abstract
In this article, we study a mathematical model for glioma cells outside tumor spheroid core. It contains matrix metalloproteases and nutrient concentrations, and takes into account of the effects of chemotaxis, haptotaxis, cell–cell adhesion, proliferation and shedding. The model consists of three semi-linear parabolic partial differential equations and an ordinary differential equation. By using the Banach fixed point theorem, the parabolic L p -theory, the parabolic Schauder estimates and the extension method, we prove that this system has a unique global solution.
Acknowledgements
The authors are supported by the NNSFC (No. 11101095).