论文标题
扩散 - 辅助的集中容量模型：位于移动曲线的对流
A concentrated capacity model for diffusion-advection: advection localized to a moving curve
论文作者
论文摘要
在这项工作中，我展示了三个空间维度中的扩散 - 添加方程如何具有其对流项弱限于位于移动曲线的速度场。这是通过集中容量的技术严格完成的，并确定了集中容量极限的形式以及解决方案的存在。该问题是由数学生物学和溶剂中蛋白质的研究激发的，在溶剂中，后者被建模为扩散量，并且将蛋白质视为1D对象，它通过接触及其自身运动来延伸溶剂。这项工作介绍了一个新颖的PDE互动框架。
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 rigorously accomplished through the technique of concentrated capacity, and the form of the concentrated capacity 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. This work introduces a novel PDE's framework for that interaction.
