Abstract and Applied Analysis
Volume 6 (2001), Issue 1, Pages 13-34
Local existence result of the single dopant diffusion including
cluster reactions of high order
Technische Universität München, Zentrum Mathematik, Arcisstr, München 21, 80290, Germany
Received 7 February 2001
Copyright © 2001 R. Bader and W. Merz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the pair diffusion process which includes cluster
reactions of high order. We are able to prove a local (in time)
existence result in arbitrary space dimensions. The model
includes a nonlinear system of reaction-drift-diffusion equations,
a nonlinear system of ordinary differential equations in Banach
spaces, and a nonlinear elliptic equation for the electrochemical
potential. The local existence result is based on the fixed point
theorem of Schauder.