Research On Spherical Symmetry Solutions To The Euler-Poisson Equations With Variable Damping Coefficients

In this thesis,we mainly study the solutions of a multi-dimensional unipolar hydrodynamic model for semiconductor devices with variable damping coefficients:where (?)?R~N(N?1) is the space variable,t?R_+=[0,?) is the time variable.This thesis is divided into four chapters.In Chapter 1,we introduce the physical background of Euler-Poisson equations,and then introduce the domestic and foreign research on Euler-Poisson equations.Finally,we introduce the research content of this paper.In Chapter 2,we study the global existence of spherical symmetry entropy solutions to the multi-dimensional Euler-Poisson equations with damping for isothermal fluids.We use a shock capturing scheme of Lax-Friedrichs type and a cut-off technique to construct approximate solutions.Finally,we establish the convergence of the approximate solutions using the method of compensated compactness and obtain the global existence of entropy solutions.In Chapter 3,by using the energy method and entropy estimation,it is shown that the entropy solutions converge to the stationary solution exponentially in time for isothermal fluids.In Chapter 4,we obtain the uniform bounded of the approximate solutions by adding artificial viscosity,introducing the improved Riemann invariants and the Maximum principle,then the viscosity vanishing method and compensated compactness framework are used to prove the global existence of spherical symmetry entropy solutions for isentropic fluids.