Analysis of Reaction-Diffusion Systems and Related Nonlinear Problems

本研究项目关注数学生态学中物种非均匀性的数学表述，如两个竞争物种的分离和入侵物种的扩散。这些现象用反应扩散方程来描述，种群密度为未知函数。我们得到了具有非线性扩散的两种模型的正稳态结构和入侵模型中自由边界问题的扩散和消失机制的令人满意的结果。

This research project is concerned with the mathematical formulation of non-uniformity of species in mathematical ecology such as the segregation of two competing species and the spreading of invasive species. These phenomena are described by reaction-diffusion equations with population densities as unknown functions. We have obtained satisfactory results on the structure of positive steady-states for two-species models with nonlinear diffusion and the mechanism of spreading and vanishing for free boundary problems in invasion models.