Electro-reaction-diffusion systems with nonlocal constraints
- Glitzky, Annegret
2010 Mathematics Subject Classification
- 35B40 35B45 35D05 35K35 35K57 35R05 78A35 80A30
- Drift-diffusion systems, reaction-diffusion systems, heterostructures, energy estimates, global estimates, asymptotic behaviour, global existence, fixed point theorems
The paper deals with equations modelling the redistribution of charged particles by reactions, drift and diffusion processes. The corresponding model equations contain parabolic PDEs for the densities of mobile species, ODEs for the densities of immobile species, a possibly nonlinear, nonlocal Poisson equation and some nonlocal constraints. Based on applications to semiconductor technology these equations have to be investigated for non-smooth data and kinetic coefficients which depend on the state variables. In two space dimensions we discuss the steady states of the system, we prove energy estimates, global a priori estimates and give a global existence result.
- Mathematischen Nachrichten 277(2004), pp.14-46