In this work I show how a diffusion-advection equation in three space-dimensions may have its advection term weakly limited to a velocity field localized to a moving curve. This is accomplished through the technique of concentrated capacity, and the form of the limit along with small time existence of solutions is determined. This problem is motivated by mathematical biology and the study of proteins in solvent where the latter is modeled as a diffusing quantity and the protein is taken to be a 1d object which advects the solvent by contact and its own motion.

中文翻译：

---

扩散平流的集中容量模型：定位于移动曲线的平流

在这项工作中，我展示了三个空间维度中的扩散平流方程如何将其平流项弱限于定位于移动曲线的速度场。这是通过集中容量技术完成的，并且确定了解决方案的小时间存在性的极限形式。这个问题是由数学生物学和溶剂中蛋白质的研究引起的，其中后者被建模为一个扩散量，蛋白质被视为一个一维物体，它通过接触和自身运动使溶剂平流。