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

Díaz Díaz, Jesús Ildefonso and Galiano, Gonzalo and Jungel, Ansgar (1999) On a quasilinear degenerate system arising in semiconductor theory. Part II: Localization of vacuum solutions. Nonlinear Analysis: Theory, Methods & Applications , 36 (5). pp. 569-594. ISSN 0362-546X

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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.

Item Type:Article
Uncontrolled Keywords:isentropic drift-diffusion model; degenerate parabolic equations; free boundary problem; local energy methods; semiconductors; drift-diffusion model; uniqueness; equations; support; space
Subjects:Sciences > Mathematics > Differential equations
ID Code:15645

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