| Titre : | Partial differential equations Vol. IV : microlocal analysis and hyperbolic equations | | Type de document : | texte imprimé | | Auteurs : | Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur | | Editeur : | New York : Springer-Verlag | | Année de publication : | 1993 | | Collection : | Encyclopaedia of Mathematical Sciences | | Importance : | 241 p. | | Présentation : | couv. ill. en coul. | | Format : | 24 cm. | | ISBN/ISSN/EAN : | 978-3-540-53363-4 | | Langues : | Anglais (eng) | | Catégories : | MATHEMATIQUES
| | Index. décimale : | 04-01 Mathématiques générales | | Résumé : | In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics. | | Note de contenu : | Contents
Chapter 1 Microlocal properties of distributions
Chapter 2 Pseudodifferential operators
Chapter 3 Fourier integral operators
Chapter 4 The propagation of singularities
Chapter 5 Solvability of (pseudo) differntial équations
Chapter 6 Smoothness of solutions of differential équations
Chapter 7 Transformation of boundary-value problems
Chapter 8 Hyperfunctions |
Partial differential equations Vol. IV : microlocal analysis and hyperbolic equations [texte imprimé] / Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur . - New York : Springer-Verlag, 1993 . - 241 p. : couv. ill. en coul. ; 24 cm.. - ( Encyclopaedia of Mathematical Sciences) . ISBN : 978-3-540-53363-4 Langues : Anglais ( eng) | Catégories : | MATHEMATIQUES
| | Index. décimale : | 04-01 Mathématiques générales | | Résumé : | In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics. | | Note de contenu : | Contents
Chapter 1 Microlocal properties of distributions
Chapter 2 Pseudodifferential operators
Chapter 3 Fourier integral operators
Chapter 4 The propagation of singularities
Chapter 5 Solvability of (pseudo) differntial équations
Chapter 6 Smoothness of solutions of differential équations
Chapter 7 Transformation of boundary-value problems
Chapter 8 Hyperfunctions |
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Partial differential equations Vol. IV / Yu. V. Egorov
