Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients by Yu.V. Egorov (PDF)

Description

This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

User’s Reviews

Editorial Reviews: Review “… Summarizing, the book presents a well-written survey of the modern theory of general PDE-s with most necessary proofs or hints, and with some explicit constructions. Therefore it will be useful for specialists in PDE-s as well as for students with basic knowledge in classical theory of PDE-s. The book is warmly recommended also to physicists, engineers and anyone interested in theory or/and applications of PDE-s.”J. Hegedüs, Acta Scientiarum Mathematicarum, Vol. 70, 2004

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐In the last two or three decades, we mathematical physicists, who study on Schroedinger operator and scattering theory, have been required to learn much about the frontier line of pure mathematics, especially about the functional analytic method of linear PDE. For the study on the classical treatment of PDE, many excellent books have already been published, e.g. Courant & Hilbert, Petrovsky. But for the modern and advanced tool of PDE, we can’t find so many exciting texts, except this Egorov’s one ! This compact text (about 200 pages) is much highly suggestive than I expected. Although this text contains only the “Elements”, many great ideas should be found even by theoretical physicists. Part two of this text, which deals with equations with constant coefficients, is especially inspiring for me, and probably for you. I can’t afford to wait to read the following series of this text.

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