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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 1, 2002, pp. 91–111
DOI: 10.4171/ZAA/1066

Published online: 2002-03-31

Local Existence Result of the Dopant Diffusion in Arbitrary Space Dimensions

R. Bader[1] and W. Merz[2]

(1) Technische Universität München, München Garching, Germany
(2) Technische Universität München, München Garching, Germany

In this paper we consider the pair diffusion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two-dimensional case. The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear ordinary differential equation in Banach spaces and an elliptic equation for the electrostatic potential. The local existence result is based on the fixed point theorem of Schauder.

Keywords: Dopant diffusion, nonlinear reaction-drift-diffusion equations, ordinary differential equations in Banach spaces

Bader R., Merz W.: Local Existence Result of the Dopant Diffusion in Arbitrary Space Dimensions. Z. Anal. Anwend. 21 (2002), 91-111. doi: 10.4171/ZAA/1066