- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 63 Issue: 2
- SELF-SIMILAR ASYMPTOTICS FOR LINEAR AND NONLINEAR MATHEMATICAL MODELS OF TUMOR ANGIOGENESIS: A REVIE...
SELF-SIMILAR ASYMPTOTICS FOR LINEAR AND NONLINEAR MATHEMATICAL MODELS OF TUMOR ANGIOGENESIS: A REVIEW
Authors : Serdal Pamuk, Irem Atac
Pages : 71-79
Doi:10.1501/Commua1_0000000712
View : 7 | Download : 4
Publication Date : 2014-08-01
Article Type : Research
Abstract :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 problemKeywords : Asymptotic solutions, governing equation, nonlinear problem