Mathematical Sciences: Problems in Nonlinear Partial Differential Equations

该项目支持研究生工作， 教授乔尔Smoller的问题，在几何部分 微分方程 特别强调的是 球对称Einstein-Maxwell和Einstein-Maxwell研究 杨-米尔斯方程 更一般地，半线性椭圆 方程和系统的对称性进行了研究， 分歧理论和破歧观点。 相关联的 利用拓扑技术研究了时间相关问题 例如连接矩阵方法。 所考虑的特定方程具有相关性 数学物理学的领域，如宇宙学，引力， 以及黑洞的形成和稳定性。

This project supports graduate students working with Professor Joel Smoller on problems in geometrical partial differential equations. Particular emphasis is placed upon the study of spherically symmetric Einstein-Maxwell and Einstein- Yang-Mills equations. More generally, semilinear elliptic equations and systems with symmetry are studied from the point of view of bifurcation theory and symmetry-breaking. The associated time dependent problems are studied using topological techniques such as the connection-matrix method. The particular equations under consideration have relevance to areas of mathematical physics such as cosmology, gravitation and the formation and stability of black holes.