Global Well-posedness Of Classical Solutions And Relaxation Limit Of The Magnetic-hydrodynamic Model For Semiconductors

This thesis is devoted to study the magnetic-hydrodynamic model for semiconductors, which takesthe form of conservation law equations for density, velocity and temperature, coupled with Maxwell’sequations. The thesis is divided into four chapters.In the first chapter, we first review the physical background and related development for themagnetic-hydrodynamic model for semiconductors. Then we list some lemmas, which will be used toprove the main results.In the second chapter, we study the global well-posdeness of classical solutions to the Cauchyproblem for the magnetic-hydrodynamic model.In the third chapter, we establish the asymptotic convergence from the non-isentropicmagnetic-hydrodynamic model to the energy-transport models from the point of view of diffusiverelaxation limits.In the fourth chapter, we summarize the problems in the thesis and give the prospect on themagnetic-hydrodynamic model.