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Partial Differential Equations II

Elements of the Modern Theory. Equations with Constant Coefficients

  • Book
  • © 1994

Overview

Editors:
  1. Yu. V. Egorov

    1. Université Paul Sabatier, Toulouse, France

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    You can also search for this editor in PubMed   Google Scholar

  2. M. A. Shubin

    1. Department of Mathematics, Northeastern University, Boston, USA

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    You can also search for this editor in PubMed   Google Scholar

  • This is a book on PDEs which is accessible to non-specialists
  • Includes supplementary material: sn.pub/extras

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Linear Partial Differential Equations. Elements of the Modern Theory

    • Yu. V. Egorov, M. A. Shubin
    Pages 1-120

  3. Linear Partial Differential Equations with Constant Coefficients

    • A. I. Komech
    Pages 121-255

  4. Wave Front of a Distribution and Simplest Theorems on Propagation of Singularities

    • Yu. V. Egorov, M. A. Shubin
    Pages 44-48

  5. Fourier Integral Operators

    • Yu. V. Egorov, M. A. Shubin
    Pages 48-60

  6. Pseudo differential Operators of Principal Type

    • Yu. V. Egorov, M. A. Shubin
    Pages 60-65

  7. Mixed Problems for Hyperbolic Equations

    • Yu. V. Egorov, M. A. Shubin
    Pages 65-78

  8. Method of Stationary Phase and Short-wave Asymptotics

    • Yu. V. Egorov, M. A. Shubin
    Pages 78-96

  9. Asymptotics of Eigenvalues of Self-adjoint Differential and Pseudodifferential Operators

    • Yu. V. Egorov, M. A. Shubin
    Pages 96-120

  10. Generalized Functions and Fundamental Solutions of Differential Equations

    • Yu. V. Egorov, M. A. Shubin
    Pages 128-149

  11. Fourier Transformation of Generalized Functions

    • Yu. V. Egorov, M. A. Shubin
    Pages 149-164

  12. Existence and Uniqueness of Solutions of Differential Equations

    • Yu. V. Egorov, M. A. Shubin
    Pages 164-185

  13. The Function P λ+ for Polynomials of Second-degree and its Application in the Construction of Fundamental Solutions

    • Yu. V. Egorov, M. A. Shubin
    Pages 185-212

  14. Boundary-value Problems in Half-space

    • Yu. V. Egorov, M. A. Shubin
    Pages 212-240

  15. Sharp and Diffusion Fronts of Hyperbolic Equations1

    • Yu. V. Egorov, M. A. Shubin
    Pages 240-250

  16. Back Matter

    Pages 257-266
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Keywords

About this book

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.

Reviews

"... 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

 

Editors and Affiliations

  • Université Paul Sabatier, Toulouse, France

    Yu. V. Egorov

  • Department of Mathematics, Northeastern University, Boston, USA

    M. A. Shubin

Bibliographic Information

  • Book Title: Partial Differential Equations II

  • Book Subtitle: Elements of the Modern Theory. Equations with Constant Coefficients

  • Editors: Yu. V. Egorov, M. A. Shubin

  • DOI: https://doi.org/10.1007/978-3-642-57876-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Hardcover ISBN: 978-3-540-52001-6Published: 14 December 1994

  • Softcover ISBN: 978-3-540-65377-6Published: 20 May 1999

  • eBook ISBN: 978-3-642-57876-2Published: 01 December 2013

  • Edition Number: 1

  • Number of Pages: VII, 266

  • Additional Information: Originally Russian edition published by VINITI, Moscow, 1988. Originally published as volume 31 in the series: Encyclopaedia of Mathematical Sciences

  • Topics: Analysis, Mathematical Methods in Physics, Numerical and Computational Physics, Simulation

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