A time-fractional Fisher-KPP equation for tumor growth: Analysis and numerical simulation
Marvin Fritz and Nikos I. Kavallaris
我们研究了一个时间分形的Fisher-KPP方程,该方程涉及Riemann-Louville分数衍生物,作用于扩散术语,由Angstmann和Henry导出(Entropy,22:1035,2020)。 该模型捕获扩散人群动力学中的记忆效应,并作为肿瘤生长建模的框架。 我们首先建立当地对薄弱解决方案的有利地位。 该分析将Ga勒金近似值与基于Bihari-Henry-Gronwall不等式的高级估计值相结合,解决了分数扩散和反应术语之间的非线性耦合。 对于小的初始数据,我们进一步证明了全球的构图和渐近稳定性。 然后提出并验证基于非均匀卷积二次方案的数值方法。 与传统配方相比,模拟表现出不同的动态行为,强调当前模型在描述肿瘤进展时的物理一致性。
We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035, 2020). The model captures memory effects in diffusive population dynamics and serves as a framework for tumor growth modeling. We first establish local well-posedness of weak solutions. The analysis combines a Galerkin approximation with a refined a priori estimate based on a Bihari-Henry-Gronwall inequality, address...
