Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 24, Issue 3, Pages 427-464Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202513500553
Keywords
Angiogenesis; chemotaxis; haptotaxis
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Funding
- Ministerio de Ciencia en Innovacion
- FEDER [MTM2009-12367, MTM2009-13655]
- Polish Ministry of Science and Higher Education [IP2011007371]
- UPM [CAM: CCG07-UPM/000-3199]
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We consider a system of differential equations modeling tumor angiogenesis. The system consists of three equations: two parabolic equations with chemotactic terms to model endothelial cells and tumor angiogenesis factors coupled to an ordinary differential equation which describes the evolution of the fibronectin concentration. We study global existence of solutions and, under extra assumption on the initial data of the fibronectin concentration we obtain that the homogeneous steady state is asymptotically stable.
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