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Stability of semiconductor states with insulating and contact boundary conditions. (English) Zbl 1148.82030
Summary: We prove the existence of global smooth solutions near a given steady state of the hydrodynamic model of the semiconductors in a bounded domain with physical boundary conditions. The steady state and the doping profile are permitted to be of large variation but the initial velocity must be small. Two cases are considered. In the first one the problem is three-dimensional, the boundary conditions are insulating and the steady state velocity vanishes. In the second one, the problem is one-dimensional, the boundary is of contact type and the steady state velocity does not vanish.

MSC:
82D37 Statistical mechanical studies of semiconductors
35B35 Stability in context of PDEs
35Q35 PDEs in connection with fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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