19th GAMM-Seminar Leipzig on
High-dimensional problems - Numerical treatment and applications

Max-Planck-Institute for Mathematics in the Sciences
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  19th GAMM-Seminar
January, 23th-25th, 2003
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  Abstract Hans-Christoph Kaiser , Sat, 10.30-10.55 Previous Contents Next  
  Classical solutions of van Roosbroeck's equations with discontinuous coefficients and mixed boundary conditions on two dimensional space domains
Hans-Christoph Kaiser (WIAS Berlin )

Van Roosbroeck's equations describe the motion of electrons and holes in semiconductor devices. The system of these equations admits a unique, local in time solution in a space of functions over a two-dimensional spatial domain which are absolutely integrable to some exponent p>1. A large variety of recombination terms, including nonlocal ones, is admissible. This theorem is derived from results in [1] about classical solutions of quasilinear parabolic systems on two dimensional domains by reformulating van Roosbroeck's system as a quasilinear parabolic system for the electro-chemical potentials of electrons and holes. This treatment of van Roosbroeck's system is consistent with a balance principle formulation of the equations and allows to justify their approximation using finite volume discretization schemes.

[1] H.-Chr. Kaiser, H. Neidhardt, and J. Rehberg, Classical solutions of quasilinear parabolic systems on two dimensional domains, Preprint 765, Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D-10117 Berlin, Germany, 2002.

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