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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 143-148 (février 2008)
Doi : 10.1016/j.crma.2007.12.001
Received : 19 September 2007 ;  accepted : 6 December 2007
Non-homogeneous boundary conditions for a fourth-order diffusion equation
Conditions aux limites non-homogènes pour une équation diffusive quantique stationnaire en une dimension
 

Pablo Amster a , Ansgar Jüngel b , Daniel Matthes c
a Departamento de Matemática, Cuidad Universitaria, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina 
b Institut für Analysis und Scientific Computing, TU Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria 
c Departimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy 

Abstract

The existence of classical solutions to a one-dimensional non-linear fourth-order elliptic equation arising in quantum semiconductor modeling is proved for a class of non-homogeneous boundary conditions using degree theory. Furthermore, some non-existence results for other classes of boundary conditions are presented. To cite this article: P. Amster et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Résumé

L’existence des solutions classiques pour une équation élliptique non-linéaire d’ordre quatre en une dimension, qui apparaît dans la modélisation des semi-conducteurs quantiques, est démontrée pour une classe de conditions aux limites non-homogènes en utilisant la théorie du degré. En plus, des résultats de non-existence pour d’autres classes de conditions aux limites sont établis. Pour citer cet article : P. Amster et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.


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