A concentrated capacity model for diffusion-advection: Advection localized to a moving curve

[摘要] 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.& nbsp; (c) 2021 The Author. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

[发布日期] 2021-09-25

[关键词] Concentrated capacity;PDE's with measure coefficients;Mathematical biology