Hsiao's pde theory on semi-conductor and plasma and their applications

Appreciating of the contributions on PDE of Professor Ling Hsiao, we review Hsiao's PDE theory on semiconductor and plasma and their applications. As an example of application of Hsiao's PDE theory on semiconductor and plasma, we study the asymptotic regimes of the compressible Euler-Maxwell equations on plasma. The derivation of the one fluid non-isentropic Euler-Maxwell system from the two-fluid model in terms of the asymptotic expansion method is performed, and the mathematical analysis of the stability of both constant equilibrium solutions and non-constant equilibrium solutions is given on T-3 or R-3.