Abstract and Applied Analysis
Volume 2008 (2008), Article ID 239870, 19 pages
doi:10.1155/2008/239870
Research Article
An Existence Result to a Strongly Coupled Degenerated System
Arising in Tumor Modeling
1Faculté des Sciences, Université de Blida, BP 270, Blida 09000, Algeria
2Ecole Polytechnique, CMAP, CNRS, 91128 Palaiseau Cedex, France
3Faculté de Mathématiques, Université des Sciences et de la Technologie Houari Boumediene, BP 32 El Alia, Alger 16111, Algeria
Received 21 March 2008; Revised 25 August 2008; Accepted 30 October 2008
Academic Editor: Nobuyuki Kenmochi
Copyright © 2008 L. Hadjadj et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider a mathematical model to describe the growth of a vascular tumor including tumor cells, macrophages, and blood vessels. The resulting system of equations is reduced to a strongly 2×2 coupled nonlinear parabolic system of degenerate type. Assuming the initial data are far enough from 0, we prove existence of a global weak solution with finite entropy to the problem by using an approximation procedure and a time discrete scheme.