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Hardback. Zustand: New. This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves.The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrodinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.…

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Zustand: Hervorragend. Zustand: Hervorragend | Seiten: 348 | Sprache: Englisch | Produktart: Bücher | 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.…

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Taschenbuch. Zustand: Neu. Partial Differential Equations and Functional Analysis | Mark Vishik: Life and Scientific Legacy | Andrew Comech (u. a.) | Taschenbuch | Trends in Mathematics | x | Englisch | 2024 | Springer | EAN 9783031336836 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.…

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

Hardback. Zustand: New. This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves.The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrodinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.…

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Hardcover. Zustand: Brand New. 348 pages. 9.25x6.10x0.98 inches. In Stock.

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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 348 pp. Englisch.…

Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 348 pp. Englisch.…

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Gebunden. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Commemorates a leading figure in the Moscow mathematical schoolIncludes personal reminiscencesFeatures review articles on Vishik s workMark Vishik was one of the prominent figures in the theory of partial differential equations.…

Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 348 pp. Englisch.…

Buch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 348 pp. Englisch.…

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