Sixin Qian

Date of Graduation


Document Type



We study the three dimensional simplified hydrodynamic model of semi-conductors where the equations of energy conservation are eliminated by assuming a pressure-density relation. The system is a combination of three hyperbolic equations coupled with an elliptic one. We prove the linear stability and the existence of local classical solutions to the initial boundary value problem for this system. The Neumann condition corresponds to an insulated boundary. Because a compatible condition is required in solving the Neumann BVP (Boundary Value Problem), a special iteration scheme is introduced to handle this situation. Based on the existence of the classical solutions to this system, we consider the initial boundary value problem when the initial data has a jump discontinuity along a smooth compact surface in t = 0, and show that the problem has a solution which is discontinuous along a hypersurface M and smooth on either side of M.