Local existence result of the single dopant diffusion including cluster reactions of high order (Q1608777)

Summary: 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. For an almost identical version of this paper see [Z. Anal. Anwend. 21, No. 1, 91-111 (2002; Zbl 0999.35002)].