两相肿瘤液流的渐近分析。弱耦合情况
Asymptotic analysis of a biphase tumor fluid flow. The weak coupling case
摘要：
本文的目的是调查的渐近行为的两相肿瘤流体流动的2尺度均匀化技术在最近的作品。该双相流体流动模型考虑了毛细血管壁渗透性和间质无血管相，两者在极限均质化问题中混合。当血管壁变得更具渗透性，我们表明，两相流体流动表现出边界层，使计算的全部问题昂贵和不稳定。在极限情况下，除了在边界附近应用不同的边界条件外，毛细压力和间隙压力都是一致的。由于严格的渐近分析，我们证明了解决方案的完整的问题，可以接近在任何阶的近似由一个单相模型与适当的边界条件的肿瘤边界和适当的校正项附近的边界。球面几何条件下的数值模拟验证了理论结果。
英文摘要：
The aim of this paper is to investigate the asymptotic behavior of a biphase tumor fluid flow derived by 2-scale homogenisation techniques in recent works. This biphase fluid flow model accounts for the capillary wall permeability, and the interstitial avascular phase, both being mixed in the limit homogenised problem. When the vessel walls become more permeable, we show that the biphase fluid flow exhibits a boundary layer that makes the computation of the full problem costly and unstable. In the limit, both capillary and interstitial pressures coincide except in the vicinity of the boundary where different boundary conditions are applied. Thanks to a rigorous asymptotic analysis, we prove that the solution to the full problem can be approached at any order of approximation by a monophasic model with appropriate boundary conditions on the tumor boundary and appropriate correcting terms near the boundary are given. Numerical simulations in spherical geometry illustrate the theoretical results.
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