Mark Iosifovich Vishik and His Work:
Award Ceremony of the Honorary Doctorate
at the Free University of Berlin

Bernold Fiedler (ed.)
Institut für Mathematik I, Freie Universität Berlin
Arnimallee 2-6, 14195 Berlin, Germany

Mark Vishik: An Honorary Doctorate Louis Nirenberg
	Louis Nirenberg

A Letter

Mark Vishik is a truly original and superb mathematician. He has made many fundamental contributions in the theory of partial differential equations (PDE) together with deep applications in fluid dynamics. He has been a world leader in these subjects for over a half century. All of us in the field have been strongly influenced by his work. He has published 250 papers and several books, and I can comment on only a small part of his work.

Vishik's early papers were on elliptic PDE--he introduced the concept of strong ellipticity--for which he obtained fundamental results. He has important work on such equations involving a small parameter. He also has seminal work on initial value problems under various boundary conditions. With L. A. Lyusternik he wrote a series of papers on a variety of problems including nonlinear problems. His papers on nonlinear elliptic and parabolic problems have had great influence. His papers with G. I. Eskin and with M. S. Agranovich are excellent. His work truly covers all aspects of PDE, linear and nonlinear, and also pseudo-differential operators; and all that is just early work. I could go on and on but let me turn to more recent things.

In the 70's Vishik published a series of important papers on differential equations involving infinitely many independent variables. Since then most of his work has been devoted to nonlinear problems--especially elliptic and parabolic ones. He treated an enormous variety of deep problems-truly astonishing. Especially striking are his papers connected with fluid dynamics and I would like to call special attention to the many papers on asymptotic behavior of solutions, in particular, attractors for PDE. These, some with A. V. Babin, are absolutely fundamental in the study of attractors; they are world famous. Their 1992 book is a principal reference. They obtained very strong estimates for the dimensions of the set of attractors for Navier-Stokes equations in fluid dynamics and for reaction-diffusion equations. Especially remarkable for the former is the estimate, from below, of the dimension. Their work on how attractors depend on various physical parameters is basic. They also studied long time behavior of solutions for nonlinear hyperbolic equations which have a Lyapounov function.

Mark Vishik continues to do absolutely first class mathematics. He is truly a world leader in PDE as well as applications. Any university honors itself in awarding him an honorary doctorate.

A Personal Remark

It is an enormous pleasure for me to participate in the wonderful honorary-doctorate celebration for Mark Vishik's 80th birthday.

As we all know, Mark is a world master in the theory of attractors. However, for us, the main attractor is Mark himself.

I first learnt of Mark's work from his theory of strong elliptic systems, which opened new doors in partial differential equations (PDE); he is a giant in the field of PDE, but I won't talk about his research.

I have lovely memories of our first meeting in 1963: it was at a conference in Novosibirsk. We became friends immediately. I felt completely at home with him. Afterwards, every time I visited Moscow, Mark and Asya have welcomed me into their home. I am always touched by their warmth and hospitality, and feel as though I am part of their family.

Many years ago at a party, a young woman claimed to be able to read palms. She read mine and told me that when I became old I would be rich. I laughed, of course, but now I think she was right: I am rich, not in money, but in friends. The same is true of Mark and Asya.

Mark, may you continue to thrive, do beautiful mathematics, and listen to music.

Continue reading with the personal greetings of Konrad Gröger.