Osmotic Cell Swelling: Modelling and Analysis

我们项目的目标是用数学方法研究描述分离两种液相的半透膜变形的多维移动边界问题。这些模型主要是在生物数学背景下讨论的，其中细胞的渗透性肿胀已经被研究。这些模型背后的数学结构是由具有无限多自由度的非线性动力系统给出的。在过去的三十年里，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，解决数学模型的适定性、稳态的稳定性和分岔特性，以及确定可能的爆炸机制等问题。

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.