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.