[AN] Michael Kniely: Thermodynamically Correct Models for Electro-Energy-Reaction-Diffusion Systems

26 November 2024 12:30 till 13:45 - Location: EEMCS Lecture Hall D@ta | Add to my calendar

We introduce a thermodynamically consistent framework for reaction-diffusion systems modeling the evolution of a finite number of charged species. This approach covers, in particular, a large class of inorganic semiconductor-type models. Here, thermodynamical consistency refers to charge and energy conservation and the production of entropy. This is achieved by formulating the model as a gradient flow system in Onsager form (for the concentrations and the internal energy) coupled to Poisson's equation (for the electrostatic potential).

First, we will focus on the structure of the Onsager operator and its relation to the electrostatic potential. Similarities and differences to other temperature-dependent semiconductor-type models shall be discussed as well. Another aspect is the well-posedness of the corresponding equilibrium problem. By resorting to the Lagrange formalism, one can rewrite this entropy maximization problem under the constraints of charge and energy conservation as a convex minimization problem. We will see that this problem admits a unique solution, hence, a unique thermodynamic equilibrium exists. This project is joint work with Katharina Hopf and Alexander Mielke.