论文信息 - A Spherically Symmetric Model for the Tumor Growth

A Spherically Symmetric Model for the Tumor Growth

The nonlinear tumor equation in spherical coordinates assuming that both the diffusivity and the killing rate are functions of concentration of tumor cell is studied. A complete classification with regard to the diffusivity and net killing rate is obtained using Lie symmetry analysis. The reduction of the nonlinear governing equation is carried out in some interesting cases and exact solutions are obtained.

Ashfaque H. Bokhari | Fiazud Din Zaman | Saeed M. Ali | Muhammad Yousuf

[1] G. Bluman,et al. Symmetries and differential equations , 1989 .

[2] Gregory J. Reid,et al. New classes of symmetries for partial differential equations , 1988 .

[3] J. Murray,et al. A mathematical model of glioma growth: the effect of chemotherapy on spatio‐temporal growth , 1995, Cell proliferation.

[4] B. Cantwell,et al. Introduction to Symmetry Analysis , 2002 .

[5] Ashfaque H. Bokhari,et al. On the solutions and conservation laws of the model for tumor growth in the brain , 2009 .

[6] G. Bluman,et al. Applications of Symmetry Methods to Partial Differential Equations , 2009 .

[7] G. Bluman,et al. Symmetry and Integration Methods for Differential Equations , 2002 .

[8] D. S. Jones,et al. Differential Equations and Mathematical Biology , 1983 .

[9] Symmetry classifications and reductions of some classes of (2+1)-nonlinear heat equation , 2008 .

[10] Philippe Tracqui,et al. THE MODELLING OF DIFFUSIVE TUMOURS , 1995 .

[11] Sibusiso Moyo,et al. Symmetry Methods Applied to a Mathematical Model of a Tumour of the Brain , 2004 .