论文标题
在具有分数时间衍生物的次延伸性肿瘤生长模型上
On a subdiffusive tumour growth model with fractional time derivative
论文作者
论文摘要
在这项工作中，我们介绍并分析了耦合部分微分方程的系统，该系统在肿瘤的影响下对肿瘤的生长进行了模拟，机械效应，营养供应和化学疗法的影响。该系统的细胞扩散是由肿瘤细胞体积分数的方程式中的时间分数衍生物建模的。营养物质和化学治疗剂的质量密度是由反应扩散方程建模的。我们通过FAEDO-GALERKIL方法和适当的紧凑度定理的应用证明了模型弱解决方案的存在和独特性。最后，我们提出了一个完全离散的系统，并说明了分数衍生物的影响以及分数参数在数值示例中的影响。
In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply, and chemotherapy. The subdiffusion of the system is modelled by a time fractional derivative in the equation governing the volume fraction of the tumour cells. The mass densities of the nutrients and the chemotherapeutic agents are modelled by reaction diffusion equations. We prove the existence and uniqueness of a weak solution to the model via the Faedo--Galerkin method and the application of appropriate compactness theorems. Lastly, we propose a fully discretised system and illustrate the effects of the fractional derivative and the influence of the fractional parameter in numerical examples.
