R. Bader, W. Merz, "Local existence result of the single dopant diffusion including cluster reactions of high order", Abstract and Applied Analysis, vol. 6, Article ID 816730, 22 pages, 2001. https://doi.org/10.1155/S108533750100046X
Local existence result of the single dopant diffusion including cluster reactions of high order
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.
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