Differential equations and elliptic inequalitties

我的nserc支持的研究有助于研究一些建模常微分方程和一些二阶椭圆不等式。这些建模方程来源于力学、生物力学和流体动力学。例如，它们包括描述球帽大挠度膜响应的奇异二阶常微分方程；描述人体脊柱在肌肉力和其他横向载荷作用下的侧向弯曲的高阶常微分方程；在边界层理论中出现的福克纳-斯坎方程，描述微粘性不可压缩流体通过楔形体的二维稳定流动。为了给偏微分不等式领域的一个悬而未决的问题一个部分的答案，将建立一个新的变分不等式理论。

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.