On a quasilinear degenerate system arising in semiconductor theory. Part II: Localization of vacuum solutions

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Galiano, Gonzalo
Jungel, Ansgar
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Pergamon Elsevier Science Ltd
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The temporal and spatial localization of vacuum sets of the solutions to the drift-diffusion equations for semiconductors is studied in this paper. It is shown that if there are vacuum sets initially then there are vacuum sets for a small time, which shows the finite propagation speed of the support of the densities. It is also shown that for a certain recombination-generation rate there is no dilation of the initial support, and under some condition on the recombination-generation rate the vacuum will develop after a certain time even if there is no vacuum initially. These results are proved based on a local energy method for free boundary problems.
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