Research Article
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Year 2019, Volume: 2 Issue: 2, 45 - 48, 30.11.2019
https://doi.org/10.34088/kojose.635255

Abstract

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.

Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis

Year 2019, Volume: 2 Issue: 2, 45 - 48, 30.11.2019
https://doi.org/10.34088/kojose.635255

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.

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.
There are 8 citations in total.

Details

Primary Language English
Subjects Software Engineering (Other)
Journal Section Articles
Authors

Melike Keleş This is me 0000-0002-7457-5873

Serdal Pamuk 0000-0002-0934-9976

Publication Date November 30, 2019
Acceptance Date November 27, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Keleş, M., & Pamuk, S. (2019). Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis. Kocaeli Journal of Science and Engineering, 2(2), 45-48. https://doi.org/10.34088/kojose.635255