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Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type

  • Book
  • © 2004

Overview

Authors:
  1. Samuil D. Eidelman

    1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine

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  2. Anatoly N. Kochubei

    1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine

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  3. Stepan D. Ivasyshen

    1. Department of Mathematical Physics, National Technical University of Ukraine Kiev Polytechnical Institute, Kiev, Ukraine

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  • First book devoted to new classes of parabolic differential and pseudo-differential equations extensively studied in the last decades, such as parabolic systems of a quasi-homogeneous structure, degenerate equations of the Kolmogorov type, pseudo-differential parabolic equations, and fractional diffusion equations
  • Many of these equations are important both for other branches of mathematics, and for applications in physics

Part of the book series: Operator Theory: Advances and Applications (OT, volume 152)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
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  2. Equations. Problems. Results. Methods. Examples

    • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen
    Pages 1-52

  3. Parabolic Equations of a Quasi-Homogeneous Structure

    • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen
    Pages 53-175

  4. Degenerate Equations of the Kolmogorov Type

    • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen
    Pages 177-264

  5. Pseudo-Differential Parabolic Equations with Quasi-Homogeneous Symbols

    • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen
    Pages 265-319

  6. Fractional Diffusion Equations

    • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen
    Pages 321-361

  7. Back Matter

    Pages 363-390
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Keywords

About this book

The theory of parabolic equations, a well-developed part of the contemporary partial differential equations and mathematical physics, is the subject theory of of an immense research activity. A continuing interest in parabolic equations is caused both by the depth and complexity of mathematical problems emerging here, and by its importance in specific applied problems of natural science, technology, and economics. This book aims at a consistent and, as far as possible, a complete exposition of analytic methods of constructing, investigating, and using fundamental solutions of the Cauchy problem for the following four classes of linear parabolic equations with coefficients depending on all variables: -7 E : 2b-parabolic partial differential equations (parabolic equations of a qua- l homogeneous structure), in which every spatial variable may have its own to the time variable. weight with respect E : degenerate partial differential equations of Kolmogorov's structure, which 2 generalize classical Kolmogorov equations of diffusion with inertia. E3: pseudo-differential equations with non-smooth quasi-homogeneous symbols. E : fractional diffusion equations. 4 These classes of equations generalize in various directions the classical equations and systems parabolic in the Petrovsky sense, which were defined in [180] and studied in a number of monographs [83, 45, 146, 107, 76] and survey articles [102, 1, 215, 70, 46].

Authors and Affiliations

  • Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    Samuil D. Eidelman, Anatoly N. Kochubei

  • Department of Mathematical Physics, National Technical University of Ukraine Kiev Polytechnical Institute, Kiev, Ukraine

    Stepan D. Ivasyshen

Bibliographic Information

  • Book Title: Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type

  • Authors: Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-7844-9

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2004

  • Hardcover ISBN: 978-3-7643-7115-9Published: 27 September 2004

  • Softcover ISBN: 978-3-0348-9592-7Published: 01 November 2012

  • eBook ISBN: 978-3-0348-7844-9Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: IX, 390

  • Topics: Partial Differential Equations, Operator Theory, Mathematical Methods in Physics

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