On the Qualitative Analysis of the Uniqueness of the Movement of Endothelial Cells
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.
Anahtar Kelimeler:
Existence; uniqueness; tumor angiogenesis; steady-state solution; transition probability density function.
On the Qualitative Analysis of the Uniqueness of the Movement of Endothelial Cells
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.
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- Department of Mathematics, University of Kocaeli Umuttepe Campus, 41800, Kocaeli-TURKEY e-mail: erdemath@gmail.com Serdal PAMUK
- Department of Mathematics, University of Kocaeli Umuttepe Campus, 41800, Kocaeli-TURKEY e-mail: spamuk@kocaeli.edu.tr
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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On the Qualitative Analysis of the Uniqueness of the Movement of Endothelial Cells