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…mehr
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.
Dr. Holger Reinisch, Universitätsprofessor, Lehrstuhl für Wirtschaftspädagogik, Wirtschaftswissenschaftliche Fakultät, Friedrich-Schiller-Universität Jena; Dr. Klaus Beck, Universitätsprofessor, Lehrstuhl für Wirtschaftspädagogik, Fachbereich Rechts- und Wirtschaftswissenschaften, Johannes Gutenberg-Universität Mainz; Dr. Manfred Eckert, Universitätsprofessor, Institut für Berufspädagogik und berufliche Weiterbildung, Universität Erfurt; Dr. Tade Tramm Universitätsprofessor, Institut für Berufs- und Wirtschaftspädagogik, Universität Hamburg.
Inhaltsangabe
I. Microlocal Analysis.- II. Linear Hyperbolic Equations.- Author Index.
