Geometric asymptotics for nonlinear PDE, I / V. P. Maslov, G. A. Omelʹyanov ; transl. by Dmitrii ChibisovType de document : MonographieCollection : Translations of mathematical monographs, 202Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 2001Description : 1 vol. (VIII-285 p.) : ill. ; 25 cmISBN: 0821821091.ISSN: 0065-9282.Bibliographie : Bibliogr. p. 275-285.Sujet MSC : 35Q51, PDEs of mathematical physics and other areas of application, Soliton equations
35Q30, PDEs of mathematical physics and other areas of application, Navier-Stokes equations
81Q20, General mathematical topics and methods in quantum theory, Semiclassical techniques, including WKB and Maslov methods
37K55, Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems, Perturbations, KAM
35R35, Miscellaneous topics in partial differential equations, Free boundary problems for PDEsEn-ligne : Zentralblatt | MathSciNet | AMS Item type: Monographie
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Bibliogr. p. 275-285
The book develops asymptotic methods for the study of partial differential equations (PDE) related to nonlinear dynamics. Special consideration is given to soliton-type and smooth shock waves. The material is very useful for studies in both nonlinear dynamics and the theory of PDE.
Publisher's description: "This book is intended to provide engineering and/or statistics students, communications engineers, and mathematicians with the firm theoretic basis of source coding (or data compression) in information theory. Although information theory consists of two main areas, source coding and channel coding, the authors choose here to focus only on source coding. The reason is that, in a sense, it is more basic than channel coding, and also because of recent achievements in source coding and compression. An important feature of the book is that whenever possible, the authors describe universal coding methods, i.e., the methods that can be used without prior knowledge of the statistical properties of the data. The authors approach the subject of source coding from the very basics to the top frontiers in an intuitively transparent but mathematically sound manner.
"The book serves as a theoretical reference for communication professionals and statisticians specializing in information theory. It will also serve as an excellent introductory text for advanced-level and graduate students taking elementary or advanced courses in telecommunications, electrical engineering, statistics, mathematics, and computer science.''
Contents: Introduction; Waves in one-dimensional nonlinear media; Nonlinear waves in multidimensional media; Asymptotic solutions of some pseudodifferential equations and dynamical systems with small dispersion; Problems with a free boundary; Multi-phase asymptotic solutions; Asymptotics of stationary solutions to the Navier-Stokes equations describing stretched vortices; List of equations; Bibliography. (MathSciNet)