Mathematical Sciences: Mathematical Problems in EvolutionaryEcology and Electrochemistry

本项目由两个部分组成：a)在研究简单遗传群体的自然选择和扩散中使用反应扩散方程，b)电化学中电场影响下溶剂中带电离子的分布。进化部分通过允许个体适应度和种群大小变化来扩展Fisher在种群遗传学中的经典模型。因此，出现了一些数学上的复杂性；例如，得到的方程组不具有极大值原则。这一点，以及其他技术问题将在本研究中得到解决。

This project consists of two components: a) the use of reaction-diffusion equations in the study of natural selection and diffusion in simple genetic populations, and b) the distribution of charged ions in solvents under the influence of electric fields in electrochemistry. The evolutionary part extends Fisher's classical model in population genetics by allowing the fitness of the individuals and the population size to vary. Consequently, a number of mathematical complications arise; e.g., the resulting system of equations does not have a maximum principle. This, and other technical issues will be addressed in this research.