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The relaxation of the hydrodynamic model for semiconductors to the drift-diffusion equations. (English) Zbl 0970.35150
The authors establish the convergence and consistency of approximate solutions derived by the modified Godunov scheme for the initial-boundary value problem corresponding to a simplified one-dimemsional hydrodynamic model for semiconductors using the compensated compactness method. The trace of weak solutions is introduced, and then the weak solutions are proved to satisfy the natural boundary conditions. The zero relaxation limit of the hydrodynamic model to the drift-diffusion model is proved when the momentum relaxation time tends to zero.
Reviewer’s remark: The paper contains substantial results in the theory of electromagnetism and optics.

MSC:
35Q60 PDEs in connection with optics and electromagnetic theory
82D37 Statistical mechanical studies of semiconductors
35Q35 PDEs in connection with fluid mechanics
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