×

Local existence result of the single dopant diffusion including cluster reactions of high order. (English) Zbl 0999.35001

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)].

MSC:

35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35Q60 PDEs in connection with optics and electromagnetic theory

Citations:

Zbl 0999.35002