Partial Differential Equations IV

Microlocal Analysis and Hyperbolic Equations
1. Auflage. Softcover version of original hardcover Auflage 1993
ISBN: 978-3-642-08099-9
Verlag: Springer

Buch, Englisch, Band 33, 244 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 394 g

Reihe: Encyclopaedia of Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Egorov, Yu. V.

Shubin, M. A.

Weitere Mitwirkende

Sinha, P.C.

Egorov, Yu.V.

Ivrii, V.Ya.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

I. Microlocal Analysis.- II. Linear Hyperbolic Equations.- Author Index.