Local Existence Result of the Dopant Diffusion in Arbitrary Space Dimensions | Zendy

Ralf M. Bader | Zendy; W. Merz | Zendy

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Local Existence Result of the Dopant Diffusion in Arbitrary Space Dimensions

Author(s) -

Ralf M. Bader,

W. Merz

Publication year - 2002

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1066

Subject(s) - mathematics , banach space , nonlinear system , mathematical analysis , a priori and a posteriori , diffusion , fixed point theorem , space (punctuation) , ordinary differential equation , reaction–diffusion system , diffusion process , differential equation , physics , computer science , philosophy , knowledge management , innovation diffusion , epistemology , operating system , quantum mechanics , thermodynamics

In this paper we consider the pair diffusion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two-dimensional case. The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear ordinary differential equation in Banach spaces and an elliptic equation for the electrostatic potential. The local existence result is based on the fixed point theorem of Schauder.

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