Abstract
The drift-diffusion equations can be studied in the framework of singular perturbation analysis as a small parameter characterizing the device goes to zero. A formal asymptotic expansion, which includes internal (and eventually boundary) layer terms can be derived by standard techniques of asymptotic analysis. We present in this paper L2 estimates for the difference between the solutions of the full system and the first term of the expansion which are valid for multi-dimensional devices close to equilibrium. These estimates are based on a uniform monotone property of the equations with respect to the small parameter and on a L∞ bound for the gradient of solutions of equations under divergence form whose coefficients are bounded, and have derivatives in one direction which are bounded with respect to all variables.
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