Ri, Jinmyong; Huang, Feimin Vacuum solution and quasineutral limit of semiconductor drift-diffusion equation. (English) Zbl 1170.35013 J. Differ. Equations 246, No. 4, 1523-1538 (2009). Summary: The first half of this paper is concerning with the nonlinear drift-diffusion semiconductor model in \(d\) \((d\leq 3\)) dimensional space. The global estimate is achieved on the evolution of support of solution and the finite speed of propagation. The proof is based on the estimate of the weighted norm with special designed weight functions. In the second half, we prove the quasineutral limit locally for 1-dimensional standard drift-diffusion model with discontinuous sign-changing doping profile. Cited in 1 Document MSC: 35B25 Singular perturbations in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 35K57 Reaction-diffusion equations 82D37 Statistical mechanics of semiconductors 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs Keywords:finite speed of propagation; evolution of support; discontinuous sign-changing doping profile PDFBibTeX XMLCite \textit{J. Ri} and \textit{F. Huang}, J. Differ. Equations 246, No. 4, 1523--1538 (2009; Zbl 1170.35013) Full Text: DOI References: [1] Antontsev, S., On the localization of solutions of nonlinear degenerate elliptic and parabolic equations, Sov. Math. Dokl., 24, 420-424 (1981) · Zbl 0496.35051 [2] Diaz, J. I.; Veron, L., Local vanishing properties of solutions of elliptic and parabolic quasilinear equations, Trans. Amer. Math. Soc., 290, 787-814 (1985) · Zbl 0579.35003 [3] Diaz, J. 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