9404341 Kan The principal investigator proposes to analyse the global wave structures for systems of conservation laws governing three-phase flows in petroleum reservoirs. Global solutions to these equations with arbitrarily large initial data will be constructed by showing the convergence of various finite difference schemes and the vanishing viscosity method. He also plans to study the eqautions governing two dimensional steady irrotational transonic gas flows past an obstacle. Solutions to the inviscid problem will be constructed by studying the convergence of the zero-viscosity limit of the corresponding viscous problem. The model equations to be studied in the first problem are qualitatively similiar to various models used in practical petroleum reservoir simulations. The mathematical study of these equations should add to our understanding of the processes of secondary and tertiary oil recovery from oil fields. The equations to be studied in the second problem can be used to describe the flow of air past an airplane wing. The mathematical studies of these equations are therefore relevant to many aerodynamics applications.
