Global existence result for pair diffusion models
- Glitzky, Annegret
- Hünlich, Rolf
2010 Mathematics Subject Classification
- 35K45 35K57 35R05 35D05 35B45 80A30
- Reaction-diffusion systems for charged particles, pair diffusion models, global existence, a priori estimates, fixed point theorems
In this paper we prove a global existence result for pair diffusion models in two dimensions. Such models describe the transport of charged particles in semiconductor heterostructures. The underlying model equations are continuity equations for mobile and immobile species coupled with a nonlinear Poisson equation. The continuity equations for the mobile species are nonlinear parabolic PDEs involving drift, diffusion and reaction terms, the corresponding equations for the immobile species are ODEs containing reaction terms only. Forced by applications to semiconductor technology these equations have to be considered with non-smooth data and kinetic coefficients additionally depending on the state variables. Our proof is based on regularizations, on a priori estimates which are obtained by energy estimates and Moser iteration as well as on existence results for the regularized problems. These are obtained by applying the Banach Fixed Point Theorem for the equations of the immobile species, and the Schauder Fixed Point Theorem for the equations of the mobile species.
- SIAM J. MATH. ANAL., Vol. 36, No. 4, pp. 1200-1225