论文标题
为血管生成模型保存高阶方案的阳性
Positivity preserving high order schemes for angiogenesis models
论文作者
论文摘要
可以描述缺氧诱导的血管生成过程，将fokker-Planck类型的整合分化动力学方程与血管生成因子的扩散方程式结合在一起。我们提出高阶阳性保留方案，以通过将渐近减少与加权基本上非振荡和强稳定性保留时间离散化来近似边缘尖端密度。我们表明，捕获了代表血管形成并扩散到低氧区域的孤子样溶液。
Hypoxy induced angiogenesis processes can be described coupling an integrodifferential kinetic equation of Fokker-Planck type with a diffusion equation for the angiogenic factor. We propose high order positivity preserving schemes to approximate the marginal tip density by combining an asymptotic reduction with weighted essentially non oscillatory and strong stability preserving time discretization. We show that soliton-like solutions representing blood vessel formation and spread towards hypoxic regions are captured.
