SELF-SIMILAR ASYMPTOTICS FOR LINEAR AND NONLINEAR MATHEMATICAL MODELS OF TUMOR ANGIOGENESIS: A REVIEW

Authors : Serdal PAMUK, İrem ATAC

Pages : 71-79

Doi:10.1501/Commua1_0000000712

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Publication Date : 2014-08-01

Article Type : Research Paper

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 problem
Keywords : Asymptotic solutions, governing equation, nonlinear problem