SELF-SIMILAR ASYMPTOTICS FOR LINEAR AND NONLINEAR MATHEMATICAL MODELS OF TUMOR ANGIOGENESIS: A REVIEW
We show that the long time asymptotic solutions of initial value problems for linear and nonlinear mathematical models of tumor angiogenesisare self-similar spreading solutions. The symmetries of the governing equationsyield three-parameter families of these solutions given in terms of their mass,center of mass, and variance. Unlike the mass and center of mass, the variance,or ”time-shift,” of a solution is not a conserved quantity for the non linear problem
Keywords:
Asymptotic solutions governing equation, nonlinear problem,
___
- G.I., Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge Univ. Press, New York, (1996).
- M.H., Giga, et.al, Progress in Nonlinear Diğerential Equations and Their Applications, 79, DOI. 10.1007-978-0-8176.4651.6-3
- J.D., Murray, Mathematical Biology, Springer, Berlin, (1993).
- S., Pamuk, Solution of the porous media equation by Adomian’s decomposition method, Physics Letters A, 344 (2005), 184-188.
- A.D., Polyanin, F.Z., Valentin, Handbook of nonlinear partial diğerential equations, Chapman & Hall/CRC, (2004).
- J.L., Vazquez, Asymptotic behavior and propagation properties of the one-dimensional *ow of gas in a porous medium, Trans. Amer. Math. Soc., 277 (1983), 507-527.
- C., Zhu and Q., Liu, Validity of the semi-in…nite tumor model in tissue optics: A Monte Carlo study, OPTICS EXPRESS 17799, Vol. 19 (2011 ), No. 18. Current address : Department of Mathematics Kocaeli University 41380 Kocaeli, TURKEY E-mail address : spamuk@kocaeli.edu.tr, irem.atac@kocaeli.edu.tr
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi