TY  - JOUR
T1  - SELF-SIMILAR ASYMPTOTICS FOR LINEAR AND NONLINEAR MATHEMATICAL MODELS OF TUMOR ANGIOGENESIS: A REVIEW
AU  - Pamuk, Serdal
AU  - Atac, İrem
PY  - 2014
DA  - August
DO  - 10.1501/Commua1_0000000712
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 71
EP  - 79
VL  - 63
IS  - 2
LA  - en
AB  - 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
KW  - Asymptotic solutions
KW  - governing equation
KW  - nonlinear problem
CR  - G.I., Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge Univ. Press, New York, (1996).
CR  - M.H., Giga, et.al, Progress in Nonlinear Diğerential Equations and Their Applications, 79, DOI. 10.1007-978-0-8176.4651.6-3
CR  - J.D., Murray, Mathematical Biology, Springer, Berlin, (1993).
CR  - S., Pamuk, Solution of the porous media equation by Adomian’s decomposition method, Physics Letters A, 344 (2005), 184-188.
CR  - A.D., Polyanin, F.Z., Valentin, Handbook of nonlinear partial diğerential equations, Chapman & Hall/CRC, (2004).
CR  - 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.
CR  - 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
UR  - https://doi.org/10.1501/Commua1_0000000712
L1  - https://dergipark.org.tr/en/download/article-file/773769
ER  -