Speaker
Description
We present a thermodynamically consistent framework for reaction-diffusion systems modeling the evolution of a finite number of charged species in a temperature-dependent setting. Thermodynamical consistency guarantees, in particular, that the fundamental laws of charge and energy conservation hold, and that the total entropy is monotone as time evolves. This is achieved by starting from an abstract gradient flow system in Onsager form coupled to Poisson's equation and by specifying various model parameters subsequently. The main goal of the talk is the derivation of an entropy-entropy production (EEP) inequality for a class of electro-energy-reaction-diffusion systems. First of all, one has to introduce an appropriate relative entropy functional and to calculate the corresponding entropy production. Taking the complexity of these functionals into account, we consider a two-level semiconductor system for electrons and holes (keeping the electrostatic and energetic coupling). Assuming that some of the involved functions are bounded, we are able to establish an EEP inequality, which entails the exponential equilibration of appropriately bounded global solutions.
