Grant: Discovery Grants Program - Individual

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. The research is of importance in applications. For example, our study on the Falkner-Skan equation is of importance in separation theory of aeronautics because separation of the boundary layer can destroy the bound vortex on lifting bodies such as airfoils. The methodologies will include some new singular integral methods, iterative techniques, rigorous analytical techniques and variational approaches. Some softwares like Maple will be applied in the research. These new integral methods can be used to treat some other applied problems like beam models and the new theory of variational inequalities has potential applications to optimization, control problems and game theory. The proposed research contributes significantly to the training and development of highly qualified personnel.