磁场中类时极值曲面运动的稳定性与分支

本项目研究磁场中类时极值曲面运动的稳定性与分支理论。主要致力于研究磁场中精确类时极值破裂曲面的存在性，稳定性以及奇性的分支理论。类时极值曲面运动模型是一类具有特殊结构的几何波动方程，它的奇性衍射稳定性理论的研究是数学物理领域中活跃且重要的研究课题之一。寻找类时极值破裂曲面的关键在于选取适当的坐标，把与磁场耦合的几何波动方程转化为一类具有特殊非线性项的拟线性常微分方程组，进而分析这类拟线性常微分方程组的解析解存在性以及相应的动力学演化。对这类问题的研究不仅能够为拟线性常微分方程组的定性理论提供全新结果，而且还能建立磁场中类时极值曲面运动的奇性衍射稳定性与分支理论。

This project is devoted to the study of the nonlinear stability and bifurcation theory for the motion of timelike extreme hypersurfaces in magnetic field. The main subject is to find the exact extremal timelike blowup hypersurfaces, then to investigate the nonlinear stability and bifurcation theory of them. The model is a class of geometric wave equations, and the nonlinear stability of singularity to them is one of most important topics in mathematics and Physics. Hence if we can find a suitable coordinates, then the geometric wave equation related to the motion of timelike extreme hypersurface in magnetic field is equivalent to a class of quasilinear ordinary differential system with completely new nonlinear terms. Furthermore, we can develop the nonlinear stability theory not only for the quasilinear ordinary differential system but also for the propagation of singularity of timelike extreme hypersurfaces in magnetic fields.