Abstract
In this paper, the initial value problem for the drift-diffusion equation which stands for a model of a semiconductor device is studied. When the dissipative effect on the drift-diffusion equation is given by the half Laplacian, the dissipation balances to the extra force term. This case is called critical. The goal of this paper is to derive decay and asymptotic expansion of the solution to the drift-diffusion equation as time variable tends to infinity.
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Communicated by Nader Masmoudi.
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Yamamoto, M., Sugiyama, Y. Asymptotic Behavior of Solutions to the Drift-Diffusion Equation with Critical Dissipation. Ann. Henri Poincaré 17, 1331–1352 (2016). https://doi.org/10.1007/s00023-015-0428-7
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DOI: https://doi.org/10.1007/s00023-015-0428-7