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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Gatenby-Gawlinski模型的一些归约化的数值研究

分析癌症的Gatenby-Gawlinski模型是分析的对象，目的是通过适当减少来研究模型工作背后的数学框架。我们从关于完整模型的简要概述开始进行数值模拟，以研究行进线的锋利度/平滑度，然后通过研究基于两方程式和基于一方程式的折减的情况进行研究。我们采用一种基于有限体积近似的数值策略，并采用空间平均波速估计量来定量地逼近行波现象。关于一个基于方程的模型，我们提出了一个在简并反应扩散方程领域内的框架，它被证明是有效的，以定性地恢复由Gatenby-Gawlinski模型引起的典型趋势。最后，