Mathematical Sciences: Analytical Problems for Models in Compressible Fluid Mechanics

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9623037 Gamba This proposal concerns problems that model potential compressible fluid flow and charged-particle transport systems. The compressible fluid flow models under consideration include the standard transonic flow problem in gas dynamics, its viscous approximations and boundary value problem, and the Mach reflection problem when a weak shock (pressure) wave collides with an oblique obstacle. Models of charged- particle transport systems are studied within the framework of submicron electronic devices. In particular these models include electro- hydrodynamic or energy-transport models for semiconductors, related models for plasmas, boundary value problems and their high field approximations. %%% Areas of applications of the proposed research include models in aerodynamics and aircraft design. In particular, wing performance just below supersonic speeds and wing design for flight in the upper atmosphere. These are models that describe how a gas moves around an object at high speeds (i.e. close to producing sonic booms). In addition models of ionized plasmas and electron transport are considered. In particular, the design and performance simulation of semiconductor devices of extremely small size and even quantum level. The models under consideration describe the flow of current in the working of a submicron or a quantum-scale electronic device. The core of the proposal focuses on issues related to questions of validity and stability of models based on the available data. This information is of paramount importance in finding the best computational strategy for the computer aided simulation of experiments. ***