Global estimates and asymptotics for electro reaction diffusion systems in heterostructures

Abstract

We treat a wide class of electro reaction diffusion systems with nonsmooth data in two dimensional domains. Forced by applications in semiconductor technology a nonlinear and nonlocal Poisson equation is involved. We state global existence, uniqueness and asymptotic properties of solutions to the evolution problem. Essential tools in our investigations are energetic estimates, Moser iteration, regularization techniques and results for electro diffusion systems with weakly nonlinear volume and boundary source terms. Especially, we discuss the connection between the existence of global lower bounds for the chemical potentials and the property that the energy functional decays exponentially to its equilibrium value as time tends to infinity

Keywords:

• reaction diffusion systems
• drift diffusion processes
• motion of charged particles
• global estimates
• existence, uniqueness
• asymptotic behaviour