LEADER 07568nam 22006975 450 001 9910751397103321 005 20240703091320.0 010 $a3-031-33681-X 024 7 $a10.1007/978-3-031-33681-2 035 $a(MiAaPQ)EBC30787882 035 $a(Au-PeEL)EBL30787882 035 $a(DE-He213)978-3-031-33681-2 035 $a(PPN)272914339 035 $a(CKB)28505217800041 035 $a(EXLCZ)9928505217800041 100 $a20231014d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPartial Differential Equations and Functional Analysis $eMark Vishik: Life and Scientific Legacy /$fedited by Andrew Comech, Alexander Komech, Mikhail Vishik 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (334 pages) 225 1 $aTrends in Mathematics,$x2297-024X 311 08$aPrint version: Comech, Andrew Partial Differential Equations and Functional Analysis Cham : Springer International Publishing AG,c2023 9783031336805 327 $aIntro -- 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 < -- < -- Partial Differential Equations and Applications> -- > -- in Honour of Mark Vishik on the Occasion of His 90th Birthday. Moscow, 2012 -- Institute for Information Transmission Problems, Moscow, June 4-7, 2012 -- < -- < -- The Scottish Book> -- > -- , 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. 327 $a1 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 ??, Independent from ? -- 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. 327 $aNumerical Observation of Soliton Asymptotics -- Adiabatic Effective Dynamics of Relativistic Solitons -- References -- The True Story of Quantum Ergodic Theorem -- References -- Bibliography of Mark Vishik -- Photographs. 330 $aMark Vishik was one of the prominent figures in the theory of partial differential equations. His ground-breaking contributions were instrumental in integrating the methods of functional analysis into this theory. The book is based on the memoirs of his friends and students, as well as on the recollections of Mark Vishik himself, and contains a detailed description of his biography: childhood in Lwów, his connections with the famous Lwów school of Stefan Banach, a difficult several year long journey from Lwów to Tbilisi after the Nazi assault in June 1941, going to Moscow and forming his own school of differential equations, whose central role was played by the famous Vishik Seminar at the Department of Mechanics and Mathematics at Moscow State University. The reader is introduced to a number of remarkable scientists whose lives intersected with Vishik?s, including S. Banach, J. Schauder, I. N. Vekua, N. I. Muskhelishvili, L. A. Lyusternik, I. G. Petrovskii, S. L. Sobolev, I. M. Gelfand, M. G. Krein, A. N. Kolmogorov, N. I. Akhiezer, J. Leray, J.-L. Lions, L. Schwartz, L. Nirenberg, and many others. The book also provides a detailed description of the main research directions of Mark Vishik written by his students and colleagues, as well as several reviews of the recent development in these directions. 410 0$aTrends in Mathematics,$x2297-024X 606 $aDifferential equations 606 $aFunctional analysis 606 $aMathematical physics 606 $aDifferential Equations 606 $aFunctional Analysis 606 $aMathematical Physics 606 $aEquacions en derivades parcials$2thub 606 $aAnàlisi funcional$2thub 608 $aLlibres electrònics$2thub 615 0$aDifferential equations. 615 0$aFunctional analysis. 615 0$aMathematical physics. 615 14$aDifferential Equations. 615 24$aFunctional Analysis. 615 24$aMathematical Physics. 615 7$aEquacions en derivades parcials 615 7$aAnàlisi funcional 676 $a515.35 676 $a515.353 700 $aComech$b Andrew$0506335 701 $aKomech$b Alexander$0472362 701 $aVishik$b Mikhail$01432949 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910751397103321 996 $aPartial Differential Equations and Functional Analysis$93578007 997 $aUNINA