Introduction to the Andro Mikelic memorial volume

Andro Mikelic passed away on 28th November 2020, after a sudden and short illness. He was a professor of Mathematics at the Institut Camille Jordan, the Mathematics Department of the University of Lyon (France), a scientist of great talent and broad range of interests and a person with brilliant individuality. Andro Mikelic was born on 2 October 1956 in Split, Croatia, a country that has always been very dear to his heart. He studied at the University of Zagreb where he obtained his PhD in Mathematics in 1983. After a few years as a researcher at the Ruder Boskovic Institute, he was a visiting professor at the University of Saint-Etienne during the academic year 1990–91, and then joined the University of Lyon as a professor in 1992.

Andro was a specialist in the theory of homogenization and the analysis of fluid mechanics equations and an expert in the modeling of flows in porous media. In particular, he is most famous for his contributions to the homogenization of the Navier–Stokes and Euler equations, which describe flows through porous media, and to the determination of effective laws at the boundary between a porous medium and a free fluid (the Beavers–Joseph–Saffman condition). He was an expert not only in deterministic homogenization but also in stochastic homogenization and he contributed to the theory of stochastic two-scale convergence in the mean and to the study of random double porosity models. He also obtained many fundamental results in various fields such as reactive transport and electrokinetic models in porous media, nonlinear filtration laws through deformable porous media (the so-called Biot model), non-Newtonian flows in complex domains, blood flow modeling, homogenization of hydrodynamics models in domains with microstructure and rough boundary.

Andro co-authored six books and authored or co-authored more than 165 scientific papers. He was a member of the editorial board of several journals, including the present one: Applicable Analysis, ESAIM Proceedings, Differential Equations and Applications, International Journal of Differential Equations. He was elected as corresponding member of the Croatian Academy of Sciences and Arts in 2014. In 2012, he was awarded the InterPore Procter and Gamble Award of the International Society for Porous Media (InterPore). He was also the recipient in 2011 of the W. Romberg Guest Professorship at the University of Heidelberg.

Andro collaborated intensively with a large number of mathematicians, physicists, chemists or engineers. He liked very much cooperative work and was very efficient at that: sharing new ideas and exploring new frontiers with his colleagues was his great pleasure. He had a remarkable ability to find and understand critical issues related to porous media and propose efficient solutions, relying on rigorous mathematical arguments. Andro was not only an experienced scientist and a dedicated colleague. He was also an extraordinary human being and a dear friend to many of us. He was a lively person by all means: his sense of humor is legendary, as well as his love of good food and, of course, of good (red and strong) wines! Working with him was thus a double experience, scientific and humanistic.

Therefore we felt it was our duty to celebrate his memory by editing this special issue of Applicable Analysis. After inviting his closest collaborators and colleagues, we received 14 contributions which, after a rigorous peer-review, appear in the present issue. They all correspond to the scientific topics cherished by Andro. More precisely, [1–4] pertain to homogenization theory, while [5,6] are concerned with Navier–Stokes equations and fluid mechanics models, [7,8] with blood flow modeling and [9–14] with various aspects of porous media. It is remarkable to see that for two contributions [11,12], Andro Mikelic is a co-author, which is a testimony of his incredible vitality and productivity until his last moments. We hope this Andro Mikelic Memorial Volume will stand as a tribute to the remembrance of his extraordinary scientific accomplishments.

Finally, we would like to thank the authors for their efforts in preparing their contributions and meeting the deadlines. We are also grateful to those whom we asked for their help in reviewing these papers. Eventually, we thank the Editors-in-Chief of the Journal for offering us the possibility to publish this special issue and for their help.

Figure 1. Andro Mikelic (1956–2020).

Disclosure statement

No potential conflict of interest was reported by the author(s).