Convergent Semidiscretization of a Nonlinear Fourth Order Parabolic System

Jüngel, Ansgar; Pinnau, René

Convergent Semidiscretization of a Nonlinear Fourth Order Parabolic System

Dateien

preprint_143.pdf(259.81 KB)

Datum

2001

Autor:innen

Jüngel, Ansgar

Pinnau, René

Schriftenreihe

Konstanzer Schriften in Mathematik und Informatik; 143

Publikationstyp

Preprint

Zusammenfassung

A semidiscretization in time of a fourth order nonlinear parabolic system in several space dimensions arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential. The resulting sequence of nonlinear second order elliptic systems admits at each time level strictly positive solutions as long as the lattice temperature is sufficiently large. Exploiting the stability of the discretization, convergence is shown in the multi-dimensional case. Under some assumptions on the regularity of the solution the rate of convergence proves to be optimal.

Fachgebiet (DDC)

004 Informatik

Zitieren

ISO 690

JÜNGEL, Ansgar, René PINNAU, 2001. Convergent Semidiscretization of a Nonlinear Fourth Order Parabolic System

BibTex

@unpublished{Jungel2001Conve-6209,
  year={2001},
  title={Convergent Semidiscretization of a Nonlinear Fourth Order Parabolic System},
  author={Jüngel, Ansgar and Pinnau, René}
}

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