On the qualitative analysis of the uniqueness of the movement of endothelial cells

ALTUNTAC E., PAMUK S.

TURKISH JOURNAL OF MATHEMATICS, cilt.34, sa.3, ss.367-375, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 3
  • Basım Tarihi: 2010
  • Doi Numarası: 10.3906/mat-0903-26
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.367-375
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.