Abstract
In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.
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Foundation item: Supported by the National Natural Science Foundation of China (11171223)
Biography: ZHOU Fang, female, Associate professor, research direction: partial differential equations.
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Zhou, F. Asymptotic behavior of solutions for the one-dimensional drift-diffusion model in the quarter plane. Wuhan Univ. J. Nat. Sci. 19, 144–148 (2014). https://doi.org/10.1007/s11859-014-0991-7
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DOI: https://doi.org/10.1007/s11859-014-0991-7