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

R. Bader and W. Merz

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.