Analysis of a mathematical model of glioma cells outside the tumor spheroid core

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.

Keywords:

• glioma cell
• global solution
• existence
• uniqueness

AMS Subject Classifications::

• 35K35
• 35Q80
• 35R05

Acknowledgements

The authors are supported by the NNSFC (No. 11101095).