On 27 and 29 October 2026, for the Crossings cycle, prof. Athanasios Tzavaras (King Abdullah University of Science and Technology - KAUST) will give the following talks:
#1
Technical Seminar: Derivation of effective equations for oscillations in hyperbolic-parabolic systems
Abstract: We present various examples of sustained oscillations for hyperbolic-parabolic systems for two paradigms: (i) Systems in nonlinear viscoelasticity with elastic strain energy that is not rank-1 convex, and (ii) the compressible Navier-Stokes system with non-monotone pressures.
The subject naturally leads to the problem of deriving effective equations for the associated homogenization problems. In contexts where oscillations appear in one scalar quantity, this problem can be addressed using ideas from the kinetic formulation for conservation laws. One derives homogenization equations for oscillations of the density in one-dimensional models of viscoelasticity with non-monotone stresses and for the compressible Navier-Stokes system with nonmonotone pressures, leading to effective systems consisting of kinetic equations coupled with the macroscopic flow.
Date and time: Tuesday 27 October, at 2:30 pm
Place: Room U3-06 (U3 Building - Piazza della Scienza 2, Milano - University of Milano-Bicocca)
#2
Math Forum: The Maxwell-Stefan system of multi-component diffusion
Abstract: The Maxwell-Stefan system is a nonlinear system of partial differential equations used in the description of diffusion processes for multi-component systems, like gases with many constituents. It was derived by Maxwell in his studies of kinetic theory and has received ample attention in the chemical engineering literature. It offers a versatile tool for modeling multicomponent diffusion, accounting for molecular interactions and diffusion mechanisms, and offers a more general and accurate model than Fick’s law, typically used in binary mixtures.
This talk will focus on the mathematical aspects of the theory of the Maxwell-Stefan. The theory is guided by the thermodynamical structure of multi-component systems and the way that the Maxwell-Stefan model emerges through a process of alignment in the high-friction limit of multi-component Euler flows. At the analysis side it uses entropy methods, and ideas from the theory of weak solutions for hyperbolic-parabolic systems. This will be a non-technical talk that will focus on: (i) Analytical issues on existence and uniqueness and the role of relative entropy. (ii) An outline of what is the Bott-Duffin inverse and its role in the Maxwell-Stefan theory. (iii) The connection between minimization of the frictional dissipation and the Maxwell-Stefan system.
Date and time: Thursday 29 October, at 3:30 pm
Place: Room Martini U6-04 (U6 Building - Piazza dell'Ateneo Nuovo 1, Milano - University of Milano-Bicocca)
An apero will follow.
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