Comptes Rendus
Ordinary Differential Equations
Non-homogeneous boundary conditions for a fourth-order diffusion equation
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 143-148.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.12.001

Pablo Amster 1; Ansgar Jüngel 2; Daniel Matthes 3

1 Departamento de Matemática, Cuidad Universitaria, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
2 Institut für Analysis und Scientific Computing, TU Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria
3 Departimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy
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Pablo Amster; Ansgar Jüngel; Daniel Matthes. Non-homogeneous boundary conditions for a fourth-order diffusion equation. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 143-148. doi : 10.1016/j.crma.2007.12.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.12.001/

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