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

Abstract

We show that the long time asymptotic solutions of initial value problems for linear and nonlinear mathematical models of tumor angiogenesis are self-similar spreading solutions. The symmetries of the governing equations yield 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 îtime-shift,î of a solution is not a conserved quantity for the nonlinear problem.