Convergent semidiscretization of a nonlinear fourth order parabolic system
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 2, pp. 277-289.

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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. 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.

DOI : 10.1051/m2an:2003026
Classification : 35K35, 65M12, 65M15, 65M20, 76Y05
Mots-clés : higher order parabolic PDE, positivity, semidiscretization, stability, convergence, semiconductors 
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     author = {J\"ungel, Ansgar and Pinnau, Ren\'e},
     title = {Convergent semidiscretization of a nonlinear fourth order parabolic system},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {277--289},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {2},
     year = {2003},
     doi = {10.1051/m2an:2003026},
     zbl = {1026.35045},
     mrnumber = {1991201},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003026/}
}
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Jüngel, Ansgar; Pinnau, René. Convergent semidiscretization of a nonlinear fourth order parabolic system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 2, pp. 277-289. doi : 10.1051/m2an:2003026. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003026/

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