An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail.
Sleeman, B. D., Anderson, A. R. A., & Chaplain, M. A. J. (1999). A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation. Applied Mathematics Letters, 12(8), 121-127. https://doi.org/10.1016/S0893-9659(99)00132-9