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.
The modelWe consider a widely general electro-reaction-diffusion system for m species X i . Let z 0 denote the electrostatic potential, and additionally let the time functions z 1 , . . . , z k be internal parameters (e.g. electrochemical potentials of species, which have been eliminated by foregoing considerations). For examples of such model equations see §8. We write z = (z 0 , z 1 , . . . , z k ). Moreover, let p i (x, z) be suitable chosen reference densities such thatwhere the functions P i depend on z only. We call the quantities We assume that the species X 1 , . . . , X l are mobile which means that they underlie drift-diffusion processes. The second group of species X l+1 , . . . , X m is assumed to be immobile, no drift-diffusion processes take place. The spatial and temporal variation of their densities is realised by reactions with mobile species and their transport processes. If the mobile and immobile species are charged they contribute to the charge density and influence the electrostatic potential z 0 . The transport of the mobile species is based on the drift-diffusion flux densitieswith diffusion coefficients D i depending on the spatial variable and on the state (b, z) and with charge numbers(1.1)The continuity equations for the mobile and immobile species contain source terms resulting from reversible mass action type reactions of the form
