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, Partial differential equations -- Equations of mathematical physics and other areas of application, Soliton-like equations
35Q30, Partial differential equations -- Equations of mathematical physics and other areas of application, Navier-Stokes equations
81Q20, Quantum theory -- General mathematical topics and methods in quantum theory, Semiclassical techniques, including WKB and Maslov methods
37K55, Dynamical systems and ergodic theory -- Infinite-dimensional Hamiltonian systems, Perturbations, KAM for infinite-dimensional systems
35R35, Partial differential equations -- Miscellaneous topics, Free boundary problemsEn-ligne : Zentralblatt | MathSciNet | AMS
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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.
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"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)