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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). © 2007 Académie des sciences.

Registro:

Documento: Artículo
Título:Non-homogeneous boundary conditions for a fourth-order diffusion equation
Autor:Amster, P.; Jüngel, A.; Matthes, D.
Filiación:Departamento de Matemática, Cuidad Universitaria, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Institut für Analysis und Scientific Computing, TU Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria
Departimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy
Año:2008
Volumen:346
Número:3-4
Página de inicio:143
Página de fin:148
DOI: http://dx.doi.org/10.1016/j.crma.2007.12.001
Título revista:Comptes Rendus Mathematique
Título revista abreviado:C. R. Math.
ISSN:1631073X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1631073X_v346_n3-4_p143_Amster

Referencias:

  • Ancona, M., Iafrate, G., Quantum correction to the equation of state of an electron gas in a semiconductor (1989) Phys. Rev. B, 39, pp. 9536-9540
  • Bleher, P., Lebowitz, J., Speer, E., Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations (1994) Commun. Pure Appl. Math., 47, pp. 923-942
  • Caceres, M., Carrillo, J.A., Toscani, G., Long-time behavior for a nonlinear fourth order parabolic equation (2005) Trans. Amer. Math. Soc., 357, pp. 1161-1175
  • Derrida, B., Lebowitz, J., Speer, E., Spohn, H., Fluctuations of a stationary nonequilibrium interface (1991) Phys. Rev. Lett., 67, pp. 165-168
  • Gualdani, M.P., Jüngel, A., Toscani, G., A nonlinear fourth-order parabolic equation with non-homogeneous boundary conditions (2006) SIAM J. Math. Anal., 37, pp. 1761-1779
  • A. Jüngel, D. Matthes, The Derrida-Lebowitz-Speer-Spohn equation: existence, non-uniqueness, and decay rates of the solutions, SIAM J. Math. Anal., in press; Jüngel, A., Pinnau, R., Global non-negative solutions of a nonlinear fourth-oder parabolic equation for quantum systems (2000) SIAM J. Math. Anal., 32, pp. 760-777
  • Lloyd, N., (1978) Degree Theory, , Cambridge University Press, Cambridge

Citas:

---------- APA ----------
Amster, P., Jüngel, A. & Matthes, D. (2008) . Non-homogeneous boundary conditions for a fourth-order diffusion equation. Comptes Rendus Mathematique, 346(3-4), 143-148.
http://dx.doi.org/10.1016/j.crma.2007.12.001
---------- CHICAGO ----------
Amster, P., Jüngel, A., Matthes, D. "Non-homogeneous boundary conditions for a fourth-order diffusion equation" . Comptes Rendus Mathematique 346, no. 3-4 (2008) : 143-148.
http://dx.doi.org/10.1016/j.crma.2007.12.001
---------- MLA ----------
Amster, P., Jüngel, A., Matthes, D. "Non-homogeneous boundary conditions for a fourth-order diffusion equation" . Comptes Rendus Mathematique, vol. 346, no. 3-4, 2008, pp. 143-148.
http://dx.doi.org/10.1016/j.crma.2007.12.001
---------- VANCOUVER ----------
Amster, P., Jüngel, A., Matthes, D. Non-homogeneous boundary conditions for a fourth-order diffusion equation. C. R. Math. 2008;346(3-4):143-148.
http://dx.doi.org/10.1016/j.crma.2007.12.001