Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis
Abstract
In
this work, we obtain the regular perturbation solutions of a mathematical model
in tumor angiogenesis in one and two space dimensions. Our results show that
the solutions we have obtained are in good agreement with the solutions
obtained by other methods. We also present our results in Matlab generated
figures.
Keywords
References
- Paweletz N., Knierim M., 1989. Tumor-related angiogenesis. Critical Reviews in Oncology, 9(3), 197-242.
- Levine H. A., Sleeman B. D., 2000. A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis. Mathematical Biosciences, 168, 77-115.
- Pamuk S., Gürbüz A., 2004. Stability analysis of the steady-state solution of a mathematical model in tumor angiogenesis. Global Analysis and Applied Mathematics, 729, 369-373.
- Pamuk S., 2003. Qualitative analysis of a mathematical model for capillary formation in tumor angiogenesis. Mathematical Models and Methods in Applied Sciences, 13(1), 19-33.
- Pamuk S., 2004. Steady-state analysis of a mathematical model for capillary network formation in the absence of tumor source. Mathematical Biosciences, 189, 21-38
- Bender C.M., Orszag S.A., 1999. Advanced Mathematical Methods for Scientists and Engineers, Springer, New York.
- Hunter J.K., 2004. Asymptotic Analysis and Singular Perturbation Theory, University of California at Davis, California.
- Rice R. G., Do D. D., 1995. Applied Mathematics And Modeling For Chemical Engineers, John Wiley and Sons Inc., New York.
Details
Primary Language
English
Subjects
Software Engineering (Other)
Journal Section
Research Article
Authors
Melike Keleş
This is me
0000-0002-7457-5873
Türkiye
Serdal Pamuk
*
0000-0002-0934-9976
Türkiye
Publication Date
November 30, 2019
Submission Date
October 21, 2019
Acceptance Date
November 27, 2019
Published in Issue
Year 2019 Volume: 2 Number: 2