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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Official URL: http://www.sciencedirect.com/science/article/pii/S0764444297839535

## Abstract

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 |
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Uncontrolled Keywords: | drift-diffusion model; two continuity equations; Poisson equation; formation of vacuum; energy methods |

Subjects: | Sciences > Mathematics > Differential geometry |

ID Code: | 15810 |

References: | S.N. Antontsev, J.I. Diaz, A.V. Domansky. Continuous dependence and stabilization of solutions of the degenerate system in two-phase filtration. Dinamika sploshnoi sredy (No. 107) (1993) S. Antontsev, J.I. Díaz, S. Shmarev. The support shrinking in solutions of parabolic equations with nonhomogeneous absorption terms Ann. Fac. Sci. Toulouse, 4 (1995), pp. 5–30 J.I. Diaz, R. Kersner. On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium. J. Differ. Equations, 69 (1987), pp. 368–403 G. Galiano. Sobre algunos problemas de la Mecánica de Medios Continuos en los que se originan fronteras libres. Tests DoctoralUniversidad Complutense de Madrid, New York (1997) A. Jüngel. A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling, to appear in Math. Nachr. (1997) A. Jüngel. Asymptotic analysis of a semiconductor model based on Fermi-Dirac statistics. Math. Meth. Appl. Sci., 19 (1996), pp. 401–424 J. Rulla. Weak solutions to Stefan problems with prescribed convection. SIAM J. Math. Anal., 18 (1987), pp. 1784–1800 |

Deposited On: | 03 Jul 2012 08:39 |

Last Modified: | 06 Feb 2014 10:32 |

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