Moving-boundary problems in blood flow

提出了血流与柔性（弹性或粘弹性）动脉之间的流体结构相互作用的研究。基础数学模型将不可压缩粘性流体的Navier-Stokes方程与描述血管壁动力学的结构方程耦合在一起。由此得到的移动边界问题具有混合双曲-抛物问题的特征。研究了一类约简问题的存在唯一性，提出了一种求解全问题的有效方法。对柔性管中的泰勒色散进行了理论和计算研究。这项工作的结果对于研究血管内纳米颗粒癌症药物递送，以及更广泛地研究人类心血管功能具有重要意义。提出了新的数学和计算技术的发展，以研究脉动人体动脉的血流。这项工作的动机是心血管和肿瘤学应用，并将与休斯顿的德克萨斯医学中心合作进行。

A study of fluid-structure interaction between blood flow and compliant (elastic or viscoelastic) arteries is proposed. The underlying mathematical model couples the Navier-Stokes equations for an incompressible, viscous fluid with the structure equations describing vessel wall dynamics. The resulting moving-boundary problem has features of a mixed, hyperbolic-parabolic problem. An existence and uniqueness study of a reduced problem, and a novel scheme for efficient computation of the full problem, are proposed. A theoretical and computational study of Taylor dispersion in compliant tubes is also proposed. Results from this work are important for a study of intravascular nano-particle cancer drug delivery, and more generally, in the study of human cardiovascular function.Development of new mathematical and computational techniques to study blood flow in pulsating human arteries is proposed. The work is motivated by cardiovascular and oncological applications, and will proceed in collaboration with the Texas Medical Center in Houston.