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

Year 2014, Volume: 63 Issue: 2, 71 - 79, 01.08.2014

Serdal Pamuk İrem Atac

https://doi.org/10.1501/Commua1_0000000712

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

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