Gatenby-Gawlinski模型某些约化的数值研究
Numerical investigation of some reductions for the Gatenby-Gawlinski model
摘要：
Gatenby-Gawlinski癌症侵袭模型是分析的对象，以研究模型背后的数学框架，通过适当的减少。我们进行数值模拟，研究的清晰度/平滑度的旅行前从一个简短的概述有关的完整的模型，并继续通过检查的情况下，基于两个方程和基于一个方程的减少。我们利用有限体积近似的数值策略，并采用空间平均波速估计来定量地接近行波现象。关于一个基于方程的模型，我们提出了一个减少框架内的退化反应扩散方程字段，这被证明是有效的，以定性地恢复Gatenby-Gawlinski模型所产生的典型趋势。最后，我们进行了一些数值试验，在一个特定的情况下，解析解是可用的。
英文摘要：
The Gatenby-Gawlinski model for cancer invasion is object of analysis in order to investigate the mathematical framework behind the model working by means of suitable reductions. We perform numerical simulations to study the sharpness/smoothness of the traveling fronts starting from a brief overview about the full model and proceed by examining the case of a two-equations-based and one-equation-based reduction. We exploit a numerical strategy depending on a finite volume approximation and employ a space-averaged wave speed estimate to quantitatively approach the traveling waves phenomenon. Concerning the one equation-based model, we propose a reduction framed within the degenerate reaction-diffusion equations field, which proves to be effective in order to qualitatively recover the typical trends arising from the Gatenby-Gawlinski model. Finally, we carry out some numerical tests in a specific case where the analytical solution is available.
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