论文标题
非线性双相混合模型：存在和独特性结果
Nonlinear biphasic mixture model: existence and uniqueness results
论文作者
论文摘要
本文涉及对数学模型的开发和分析，该模型是由间质流体动力学和组织变形力学（Poro-elasto-Hydrodnynalicals）在体外实体瘤中动机的。经典混合理论是针对两阶段系统的质量和动量平衡方程。这项研究的主要贡献是，我们将生理转运参数（即液压电阻率）视为各向异性和异质性，因此管理系统是强烈的耦合和非线性的。我们得出了一个弱的公式，然后提出了等效的定点问题。这使我们能够使用Galerkin方法，并且单调操作员的经典结果与著名的Schauder和Banach固定点定理相结合，以证明存在和唯一性结果。
This paper is concerned with the development and analysis of a mathematical model that is motivated by interstitial hydrodynamics and tissue deformation mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumor. The classical mixture theory is adopted for mass and momentum balance equations for a two-phase system. A main contribution of this study, we treat the physiological transport parameter (i.e., hydraulic resistivity) as anisotropic and heterogeneous, thus the governing system is strongly coupled and nonlinear. We derived a weak formulation and then formulated the equivalent fixed-point problem. This enabled us to use the Galerkin method, and the classical results on monotone operators combined with the well-known Schauder and Banach fixed point theorems to prove the existence and uniqueness results.
