Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type
By: by Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen
Contributors: Kochubei, Anatoly N.; Ivasyshen, Stepan D.
Series: Operator Theory: Advances and Applications -- 152; Operator theory, advances and applications -- 152.
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 2004
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 390
ISBN-13: 9783034895927; 9783034878449
Subjects: Mathematics; Mathematical physics; Operator theory; Partial Differential equations
Description: The theory of parabolic equations, a well-developed part of the contemporary theory of partial differential equations and mathematical physics, is the subject of immense research activity. A stable interest to parabolic equations is caused both by the depth and complexity of mathematical problems emerging here, and by its importance in applied problems of natural science, technology, and economics. This book aims at a consistent and, as far as possible, 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: - 2b-parabolic partial differential equations, in which every spatial variable may have its own weight with respect to the time variable - degenerate partial differential equations of Kolmogorov's structure, which generalize classical Kolmogorov equations of diffusion with inertia - pseudo-differential equations with non-smooth quasi-homogeneous symbols - fractional diffusion equations. All of these provide mathematical models for various diffusion phenomena. In spite of a large number of research papers on the subject, this is the first book devoted to this topic. It will be useful both for mathematicians interested in new classes of partial differential equations, and physicists specializing in diffusion processes.
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Table of contents: title: Preface; title: 1. Equations. Problems. Methods. Results. Examples; title: 2. Parabolic Equations of a Quasi-Homogeneous Structure; title: 3. Degenerate Equations of the Kolomogorov Type; title: 4. Pseudo-Differential Parabolic Equations with Quasi-Homogeneous Symbols; title: 5. Fractional Diffusion Equations; title: Appendix. Fox's H-Functions; title: Bibliography; title: Notation; title: Index.