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Space localization and uniqueness of solutions of a quasilinear parabolic system arising in semiconductor theory


Díaz Díaz, Jesús Ildefonso and Galiano, Gonzalo and Jungel, Ansgar (1997) Space localization and uniqueness of solutions of a quasilinear parabolic system arising in semiconductor theory. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 325 (3). pp. 267-272. ISSN 0764-4442

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A degenerate parabolic system consisting in two continuity equations for densities of charged particles and in the Poisson equation for an electric potential is considered. We show the finite speed of propagation, a waiting time property for the vacuum (null) sets and a property of formation of vacuum. The proofs are based on energy methods. Furthermore, some results on the uniqueness of solutions are proved by using different duality methods.

Item Type:Article
Uncontrolled Keywords:drift-diffusion model; two continuity equations; Poisson equation; formation of vacuum; energy methods
Subjects:Sciences > Mathematics > Differential geometry
ID Code:15810

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