Analysis of Nonlinear Problems in Hydrodynamics and Reaction-Diffusion

摘要

This research focused on fluid dynamics and hydrodynamic stability and related issues. Other work included lubrication, reaction-diffusion systems, dynamics of biochemical systems and multiphase flows. The problem on the stability and bifurcations of the flow between two rotating cylinders was studied for its simplicity, importance, and its richness in possible flow patterns. The work on lubrication studied the Reynolds equation for two-dimensional and unsteady flows. The work on biological dynamics focused on the stability of motions of cells and chemical from the point of view of morphogenesis, or the formation of patterns. Reaction-diffusion equations occur in many natural and technological situations. We studied two extensively: 1) reaction diffusion systems in biology include the release, transport and action of neurotransmitters. The effects of other chemicals that enhance or block the actions of the neurotransmitter ions have been studied. 2) the fluid dynamics of combustion processes including the stability of flows to inhomogeneities in fuel and temperature.