Gradient-Like Flow

9703497 陈 这项拟议的工作是进一步调查的某些 “梯度状”流动。特别是，重点是研究部分正则性， 唯一性和奇点的行为， 调和映射的弱流，以及调和映射的部分正则性 对于H-系的弱流， Dirichlet边界条件或自由边界 条件由于几何性质，这些流动 满足非线性偏微分方程， 很少可以通过标准PDE方法或直接 变分法 这项工作的目的是寻找新的结果， 这些问题，并开发新的研究方法 一类几何演化问题， 类似的结构。我们相信非线性 这种分析方法也可应用于材料科学，如连续铁磁体中自旋场的演化，以及其它领域。

9703497 Chen This proposed work is a further investigation of certain "gradient-like" flows. In particular, the focus is on the study of the partial regularity, the uniqueness and the behavior of the singularities for the weak flow of harmonic maps, and the partial regularity for the weak flow of H-system from a surface with a Dirichlet boundary condition or with a free boundary condition. Due to the geometric nature, these flows satisfy nonlinear partial differential equations, which rarely can be attacked by standard PDE methods or direct variational method. The aim of this proposed work is to find new results for these problems and to develop new methods for the study of a whole class of geometric evolution problems with a similar structure. The belief is that the nonlinear analysis method developed here can also be applied to material science, such as the evolution of spin fields in continuum ferromagnets, and to other areas.