Partial Differential Equations and Functional Analysis : Mark Vishik: Life and Scientific Legacy / / edited by Andrew Comech, Alexander Komech, Mikhail Vishik

• Record Nr.: UNINA9910751397103321
• Autore: Comech Andrew
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023
• ISBN: 3-031-33681-X
• Edizione: [1st ed. 2023.]
• Descrizione fisica: 1 online resource (334 pages)
• Collana: Trends in Mathematics, , 2297-024X
• Altri autori (Persone): KomechAlexander; VishikMikhail
• Disciplina: 515.35; 515.353
• Soggetti: Differential equations; Functional analysis; Mathematical physics; Differential Equations; Functional Analysis; Mathematical Physics; Equacions en derivades parcials; Anàlisi funcional; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Acknowledgments -- Introduction -- Contents -- Part I Memoirs -- Notes About My Father -- Mark Iosifovich and Asia Moiseevna: Random Reminiscences -- Meetings with Mark Iosifovich Vishik -- 1 Stefan Banach -- 2 Ivan Georgievich Petrovsky -- 3 Jacques-Louis Lions and Jean Leray -- 4 Asya Moiseevna Guterman -- Reference -- My Scientific Advisor Mark Iosifovich Vishik -- M. I. Vishik in My Life -- References -- Un Grand Mathématicien, le Professeur Vishik -- A Great Mathematician, Professor Vishik -- Recollections of a Former Mechmat Student -- A Word About M. I. Vishik -- Mark Iosifovich Vishik -- 1 Two Lessons from Mark Iosifovich -- 2 Of Classics and Romantics -- Teacher and Friend -- References -- M. I. ; Vishik -- References -- In Mark Vishik's Own Words -- Lwów -- The Departure from Lwów -- Tbilisi -- Moscow -- Dissertations -- MEI and MGU -- Reference -- Remembering Wladek Lyantse -- Part II Science -- Symposium in Honor of Professor Mark Vishik. Berlin, 2001 -- Free University of Berlin, December 17-20, 2001 -- 1 Louis Nirenberg -- A letter -- A personal remark -- 2 Roger Temam -- Some aspects of Mark's work -- References -- 3 Mark Vishik -- The sources of my work -- References -- International Conference &lt -- &lt -- Partial Differential Equations and Applications&gt -- &gt -- in Honour of Mark Vishik on the Occasion of His 90th Birthday. Moscow, 2012 -- Institute for Information Transmission Problems, Moscow, June 4-7, 2012 -- &lt -- &lt -- The Scottish Book&gt -- &gt -- , Problem 192 -- References -- General Elliptic Boundary Value Problems in Bounded Domains -- 1 Extensions of Dual Pairs -- 2 Elliptic Operators -- References -- On the Vishik-Lyusternik Method -- References -- Mark Vishik's Work on Quasilinear Equations -- Attractors for Nonlinear Nonautonomous Equations.; 1 Global Attractors for Autonomous and Nonautonomous Equations -- 2 Trajectory Attractors -- References -- Rigorous Results in Space-Periodic Two-Dimensional Turbulence -- 1 Introduction -- 2 Equations and Random Forces -- Cauchy Problem -- Markov Process and a Priori Estimates -- 3 Mixing -- Existence of a Stationary Measure -- Uniqueness and Exponential Stability -- 4 Consequences of Mixing -- Ergodic Theorems -- Random Attractors -- Dependence on Parameters and Stability -- 5 Large Deviations -- Donsker-Varadhan Type Large Deviations -- Vanishing Noise Limit -- 6 Inviscid Limit -- Properties of μν, Independent from ν -- Inviscid Limit -- 7 3d Navier-Stokes System in Thin Domains -- 8 Open Problems -- Frequently Used Notations -- References -- Attractors of Hamiltonian Nonlinear Partial Differential Equations -- 1 Introduction -- 2 Bohr's Postulates: Quantum Jumps -- 3 Schrödinger's Identification of Stationary Orbits -- 4 Coupled Maxwell-Schrödinger Equations -- 5 Bohr's Postulates via Perturbation Theory -- 6 Quantum Jumps as Global Attraction -- 7 Relation to Linear Quantum Mechanics -- 8 Conjecture on Attractors of G-Invariant Equations -- 9 Results on Global Attractors for Nonlinear Hamiltonian PDEs -- Equations with the Trivial Symmetry Group G={e} -- Group of Translations G=Rn -- Unitary Symmetry Group G=U(1) -- Orthogonal Group G=SO(3) -- 10 On Generic Equations -- 11 Adiabatic Effective Dynamics of Solitons -- Mass-Energy Equivalence -- 12 Stability of Stationary Orbits and Solitons -- Spectral Stability of Solitons -- Asymptotic Stability of Stationary Orbits: Orthogonal Projection -- Asymptotic Stability of Solitons: Symplectic Projection -- Generalizations and Applications -- Further Generalizations -- 13 Linear Dispersion -- 14 Numerical Simulation of Soliton Asymptotics -- Kinks of Relativistic-Invariant Ginzburg-Landau Equations.; Numerical Observation of Soliton Asymptotics -- Adiabatic Effective Dynamics of Relativistic Solitons -- References -- The True Story of Quantum Ergodic Theorem -- References -- Bibliography of Mark Vishik -- Photographs.
• Sommario/riassunto: 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.