Partial Differential Equations and Functional Analysis

ISBN-13: 9783031336805 / Angielski / Twarda / 2023

Opis

Mark Vishik was one of the prominent figures in the theory of partial differential equations. His ground-breaking contributions were instrumental in integrating the methods of functional analysis into this theory.

The book is based on the memoirs of his friends and students, as well as on the recollections of Mark Vishik himself, and contains a detailed description of his biography: childhood in Lwów, his connections with the famous Lwów school of Stefan Banach, a difficult several year long journey from Lwów to Tbilisi after the Nazi assault in June 1941, going to Moscow and forming his own school of differential equations, whose central role was played by the famous Vishik Seminar at the Department of Mechanics and Mathematics at Moscow State University. The reader is introduced to a number of remarkable scientists whose lives intersected with Vishik’s, including S. Banach, J. Schauder, I. N. Vekua, N. I. Muskhelishvili, L. A. Lyusternik, I. G. Petrovskii, S. L. Sobolev, I. M. Gelfand, M. G. Krein, A. N. Kolmogorov, N. I. Akhiezer, J. Leray, J.-L. Lions, L. Schwartz, L. Nirenberg, and many others.

The book also provides a detailed description of the main research directions of Mark Vishik written by his students and colleagues, as well as several reviews of the recent development in these directions.

Spis treści

- Part I Memoirs. - Notes About My Father. - Mark Iosifovich and Asia Moiseevna: Random Reminiscences. - Meetings with Mark Iosifovich Vishik. - My Scientific Advisor Mark Iosifovich Vishik. - M. I. Vishik in My Life. - Un Grand Mathématicien, le Professeur Vishik. - Recollections of a Former Mechmat Student. - A Word About M. I. Vishik. - Mark Iosifovich Vishik. - Teacher and Friend. - M. I. Vishik. - In Mark Vishik’s Own Words. - Remembering Wladek Lyantse. - Part II Science. - Symposium in Honor of Professor Mark Vishik. Berlin, 2001. - International Conference «Partial Differential Equations and Applications» in Honour of Mark Vishik on the Occasion of His 90th Birthday. Moscow, 2012. - «TheScottishBook», Problem 192. - General Elliptic Boundary Value Problems in Bounded Domains. - On the Vishik–Lyusternik Method. - Mark Vishik’s Work on Quasilinear Equations. - Attractors for Nonlinear Nonautonomous Equations. - Rigorous Results in Space-Periodic Two-Dimensional Turbulence. - Attractors of Hamiltonian Nonlinear Partial Differential Equations. - The True Story of Quantum Ergodic Theorem. - Bibliography of Mark Vishik. - Photographs.