This paper extends the work of Pamuk (2003) by showing mathematically that the movement of endothelial cells, to the regions where active enzyme is large or where fibronectin is small, is unique. To do this, we obtain the existence and uniqueness of the steady-state solution of an initial-boundary value problem which mathematically models endothelial cell movement in tumor angiogenesis. A specific example showing the instability of this steady-state solution is provided.
Existence; uniqueness; tumor angiogenesis; steady-state solution; transition probability density function.
ALTUNTAÇ, ERDEM and PAMUK, SERDAL
"On the Qualitative Analysis of the Uniqueness of the Movement of Endothelial Cells,"
Turkish Journal of Mathematics: Vol. 34:
3, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol34/iss3/7