Talks by Annamaria Massimini and Stefanos Georgiadis

Speaker #1: Annamaria Massimini
Title #1: Analysis of a Poisson–Nernst–Planck–Fermi model for ion transport in biological channels

Abstract #1: In this talk, we analyse a Poisson-Nernst-Planck-Fermi model to describe the evolution of a mixture of finite size ions in liquid electrolytes, which move through biological membranes or nanopores. The ion concentrations solve a cross-diffusion system in a bounded domain with mixed Dirichlet-Neumann boundary conditions. A drift term due to the electric potential is also present in the equations. The latter is coupled to the concentrations through a Poisson-Fermi equation. The novelty and the advantage of this model is to take into account ion-ion correlations, which is really
important in case of strong electrostatic coupling and high ion concentrations. The global-in-time existence of bounded weak solutions is proved, employing the boundedness-by-entropy method, extended to nonhomogeneous boundary conditions. Furthermore, the weak-strong uniqueness result is also presented.

Speaker #2: Stefanos Georgiadis
Title #2: Multicomponent Compressible Flows

Abstract #2: In this talk, we focus on a type-I system modeling non-isothermal multicomponent flows that include the effects of mass-diffusion and heat conduction but no viscous effects. First, we discuss how the model is obtained via a Chapman-Enskog expansion of a type-II model. The second step is to use the dissipative structure of the system, in order to verify that it fits into the general framework of systems of hyperbolic-parabolic type. Third, we derive a relative entropy identity, which is used in order to prove convergence of strong solutions of the original system, to strong solutions of heat-conducting multicomponent Euler flows when the mass-diffusivity tends to zero. Also to prove convergence to smooth solutions of multicomponent adiabatic Euler flows when both heat conductivity and mass diffusivity tend to zero. Finally, we focus on the parabolic counterpart of the system, obtained by setting the barycentric velocity equal to zero, and show the global-in-time existence of weak solutions and weak-strong uniqueness.