Stability of transonic strong shock waves for the one -dimensional hydrodynamic model for semiconductors

In this paper we study the stability of transonic strong shock solutions of the steady-state onedimensional unipolar hydrodynamic model for semiconductors. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony–Meyer and the introduction of a large parameter.