Bader, R.; Merz, W. Local existence result of the single dopant diffusion including cluster reactions of high order. (English) Zbl 0999.35001 Abstr. Appl. Anal. 6, No. 1, 13-34 (2001). 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)]. Cited in 1 Review MSC: 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) 35Q60 PDEs in connection with optics and electromagnetic theory Keywords:reaction-drift-diffusion equation; ordinary differential equations in Banach spaces; elliptic equation for the electrochemical potential; fixed point theorem of Schauder Citations:Zbl 0999.35002 × Cite Format Result Cite Review PDF Full Text: DOI EuDML