Mathematical Sciences: Mathematical Problems in Various Applied Fields

首席研究员和他的研究生将开发和使用渐近和数值方法来研究应用数学中的一些问题。特别是，他们将研究非均匀结构对声波的散射，特征值的强局域扰动，有界和无界剪切流中的扩散，以及某些平面区域上拉普拉斯算子的特征值的配对。许多自然现象都是用微分方程式来描述的，用传统的应用数学方法很难找到它们的解。主要研究人员和他的研究生将应用非标准类型的渐近和数值方法，以便准确地近似解决应用数学中不同领域的问题，如声散射和非线性扩散。

The principal investigator and his graduate students will develop and use asymptotic and numerical methods to study a number of problems in applied mathematics. In particular, they will study the scattering of sound waves by inhomogeneous structures, strong localized perturbations of eigenvalues, diffusion in bounded and unbounded shear flows, and the pairing of eigenvalues of the Laplace operator in certain planar domains. Many natural phenomena are described by differential equations whose solutions are difficult to find using traditional techniques of applied mathematics. The principal investigator and his graduate students will apply asymptotic and numerical methods of nonstandard types in order to approximate accurately the solutions of problems in diverse areas of applied mathematics such as acoustic scattering and nonlinear diffusion.