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Vacuum solution and quasineutral limit of semiconductor drift-diffusion equation. (English) Zbl 1170.35013

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.

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
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