Mathematical Sciences: Problems in Nonlinear Partial Differential Equations

主要研究人员继续研究非线性 偏微分方程 当前研究 包括非线性波解的破缺 方程，有限对称半线性方程的解 群，二维球面上的共形度量， 爱因斯坦-杨-米尔斯方程的径向对称解， 冲击波问题和某些拓扑学问题。 这些数学问题捕捉到了各种 的生理问题。 例如， 爱因斯坦-杨-米尔斯的研究对 量子效应在形成黑洞中的重要性。 数学生物学、物理学和几何学中的许多问题 都有显示特定模式或对称性的解。 对称中断指示 随着问题参数的变化，

The principal investigators continue studies of nonlinear partial differential equations. The present investigations include symmetry-breaking for solutions of nonlinear wave equations, solutions of semilinear equations with finite symmetry groups, conformal metrics on the two-dimensional sphere, radially symmetric solutions of Einstein-Yang-Mills equations, shock wave problems, and certain problems of topology. These mathematical questions capture features of a variety of physical problems. For instance, questions addressed in the Einstein-Yang-Mills studies have implications for the importance of quantum effects in forming black holes. Many problems in mathematical biology, physics, and geometry have solutions that show certain patterns or symmetries. Symmetry-breaking indicates changes in the character of the solutions as parameters of the problems change.