Differential equations and elliptic inequalitties

我的NSERC支持的研究有助于一些建模常微分方程和一些二阶椭圆不等式的研究。这些建模方程来自力学、生物力学和流体动力学。例如，它们包括奇异的二阶常微分方程描述的大挠度膜反应的球形帽;高阶常微分方程描述的横向弯曲的人的脊柱下的肌肉力量和其他横向负荷;的Falkner-Skan方程产生的边界层理论和描述的稳定的二维流动的一个轻微的粘性不可压缩流体过去楔形体。建立了一个新的变分不等式理论，部分地回答了偏微分不等式领域中的一个公开问题。

My NSERC-supported research contributes to the study of some modeling ordinary differential equations and some second order elliptic inequalities. These modeling equations arise from mechanics, biomechanics and fluid dynamics. For example, they include singular second order ordinary differential equations describing the large deflection membrane response of a spherical cap; higher order ordinary differential equations describing the lateral bending of human spine under muscle forces and other transverse loads; the Falkner-Skan equation arising in boundary layer theory and describing the steady two-dimensional flow of a slightly viscous incompressible fluid past wedge shaped bodies. A new theory of variational inequalities will be established in order to give a partial answer to an open question in the field of partial differential inequalities.