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Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type [electronic resource]

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Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type [electronic resource]
Original Title Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type [electronic resource]
Author Eidelman, Samuil D, Kochubei, Anatoly N, Ivasyshen, Stepan D
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Topics Difference equations, Difference operators, Finite differences, Numerical analysis, Difference equations, Difference operators, Finite differences, Numerical analysis
Publisher Basel : Birkha╠łuser Basel : Imprint : Birkha╠łuser
Collection folkscanomy_miscellaneous, folkscanomy, additional_collections
Language English
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Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic TypeAuthor: Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen Published by Birkh├Ąuser Basel ISBN: 978-3-0348-9592-7 DOI: 10.1007/978-3-0348-7844-9Table of Contents:Equations. Problems. Results. Methods. Examples
Parabolic Equations of a Quasi-Homogeneous Structure
Degenerate Equations of the Kolmogorov Type
Pseudo-Differential Parabolic Equations with Quasi-Homogeneous Symbols
Fractional Diffusion EquationsPreface — 1. Equations. Problems. Methods. Results. Examples — 2. Parabolic Equations of a Quasi-Homogeneous Structure — 3. Degenerate Equations of the Kolomogorov Type — 4. Pseudo-Differential Parabolic Equations with Quasi-Homogeneous Symbols — 5. Fractional Diffusion Equations — Appendix. Fox’s H-Functions — Bibliography — Notation — IndexThe 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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