β Scribed by Yu. V. Egorov (auth.), Yu. V. Egorov, M. A. Shubin (eds.)
No coin nor oath required. For personal study only.
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.
Front Matter....Pages i-vii
Microlocal Analysis....Pages 1-147
Linear Hyperbolic Equations....Pages 149-235
Back Matter....Pages 237-244
Analysis; Theoretical, Mathematical and Computational Physics
π SIMILAR VOLUMES
<p><P>Serge Alinhac (1948β) received his PhD from l'UniversitΓ© Paris-Sud XI (Orsay). After teaching at l'UniversitΓ© Paris Diderot VII and Purdue University, he has been a professor of mathematics at l'UniversitΓ© Paris-Sud XI (Orsay) since 1978. He is the author of <EM>Blowup for Nonlinear Hyperbolic
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theo
<p><P>Serge Alinhac (1948β) received his PhD from l'UniversitΓ© Paris-Sud XI (Orsay). After teaching at l'UniversitΓ© Paris Diderot VII and Purdue University, he has been a professor of mathematics at l'UniversitΓ© Paris-Sud XI (Orsay) since 1978. He is the author of <EM>Blowup for Nonlinear Hyperbolic
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theo