Department of Mathematics colloquium - Sibe Mardešić presents a sequence of lectures given by leading experts in the fields of theoretical and applied mathematics. The lectures take place at the Department of Mathematics, Faculty of Science, Bijenička cesta 30, Zagreb.

### Lecture announcement

**Time:**December 18, 2019 at 12:00AM

**Lecture room:**A001

**About the lecturer**: Andro Mikelić was born in Split, Dalmatia, Croatia where he completed his basic education. He graduated from the Faculty of Natural Sciences and Mathematics, University of Zagreb, Croatia and obtained his Ph.D. degree in mathematics in 1983 from the same university. He was awarded the Leverhulm Trust postdoctoral positions at the Imperial College, London and at the University of Sussex in 1986-1987 and the Fulbright and Humboldt scholarships in 1991 and 1992. Since 1992, he has been a Professor of applied mathematics at the Université Claude Bernard Lyon 1, Lyon, France. He became a Full Professor at same university in 2000 and a Full Distinguished Professor in 2011. From July 2002 to July 2006 he was the Vice Chairman of the Faculty of Mathematics (l'UFR Mathématiques), Université Lyon Claude Bernard Lyon 1.
From January 2011 to December 2013 he was awarded the W. Romberg Guest Professorship at the Universitat Heidelberg. In 2012, he was awarded the Interpore Procter and Gamble Award for Porous Media Research. Since June 2014, he is a corresponding member of the Croatian Academy of Sciences and Arts.
He has published more than 177 research papers with many different coauthors and his research activities include: Homogenization theory and applications (Research on homogenization of the pore level Navier- Stokes and Euler equations and equations describing multiphase flows through porous media, with the goal of finding effective filtration laws. Determination of effective constitutive laws at the interfaces porous medium / free fluid and the wall laws describing rough boundaries. Stochastic homogenization. Blood flow modeling. Reactive flows with dominant Péclet and Damkohler numbers) and PDEs in fluid mechanics.
See http://scholar.google.fr/citations?hl=fr&user=T2fX7akAAAAJ&view_op=list_works

**Lecture abstract**: The homogenization theory has been applied with success to provide effective mathematical models for the composite materials, porous media and other heterogeneous structures. By considering simultaneously models at different scales, the homogenization theory allows to derive an efficient macroscopic model which preserves the accuracy of the microscopic models. Since early seventies, it was possible to develop several analysis tools as the energy method of Tartar, the two-scale-convergence, Bloch's waves and so on. They were applied with success to problems from sciences and engineering.
Nevertheless, these techniques break down in the presence of interfaces and rough boundaries. Namely, the homogeneity is broken in the normal direction and the basic ideas of the 2-scale expansions are not applicable. The remedy consists in including the boundary layer effects. The aim of the lecture is to present results on the interface laws between porous media flows and a free viscous flows and on the computation of the effective slip over a rough boundary.