Global properties of pair diffusion models
- Glitzky, Annegret
- Hünlich, Rolf
2010 Mathematics Subject Classification
- 35B40 35B45 35K57 35R05 78A35
- Drift-diffusion systems, reaction-diffusion systems, heterostructures, energy estimates, global estimates, asymptotic behaviour
The paper deals with global properties of pair diffusion models with non-smooth data arising in semiconductor technology. The corresponding 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 containing drift, diffusion and reaction terms. The corresponding equations for the immobile species are ODEs involving reaction terms only. Starting with energy estimates obtained by methods of convex analysis we establish global upper and lower bounds for solutions of the initial boundary value problem. We use Moser iteration for the diffusing species, the non-diffusing species are treated separately. Finally, we study the asymptotic behaviour of solutions.
- Adv. Sci. Appl. 11 (2001), pp. 293-321