Osmotic Cell Swelling: Modelling and Analysis

渗透细胞膨胀：建模与分析

• 批准号: 167120965
• 负责人: Professor Dr. Joachim Escher
• 金额: --
• 依托单位: Institut für Angewandte Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/167120965?language=en
• 关键词: Osmotic; Cell; Swelling; Modelling; Analysis

The objective of our project is to mathematically investigate multi-dimensional moving boundary problems describing the deformation of semipermeable membranes separating two liquid phases. These models have been primarily discussed in a biomathematical context where osmotic swelling of cells has been investigated. The mathematical structure behind these models is given by nonlinear dynamical systems with infinitely many degrees of freedom. Significant progress in linear and nonlinear analysis in the past three decades allows to treat the full multi-dimensional problem and to address questions like well-posedness of the mathematical model, stability and bifurcation properties of steady states, as well as determing possible blow-up mechanisms.

我们的项目的目的是数学研究多维移动边界问题描述的半渗透膜分离两个液相的变形。这些模型已主要讨论了在biomethematical背景下，细胞的渗透膨胀已被调查。这些模型背后的数学结构由具有无限多个自由度的非线性动力系统给出。在过去的三十年中，线性和非线性分析取得了重大进展，可以处理完整的多维问题，并解决问题，如数学模型的适定性，稳定性和稳定状态的分叉特性，以及确定可能的爆破机制。