Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type

Samuil D. Eidelman, Stepan D. Ivasyshen, Anatoly N. Kochubei - Collection Operator theory advances and applications

386 pages, parution le 07/10/2004

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Résumé

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.

Sommaire

Preface
Equations. Problems. Methods. Results. Examples
Parabolic Equations of a Quasi-Homogeneous Structure
Degenerate Equations of the Kolomogorov Type
Pseudo-Differential Parabolic Equations with Quasi-Homogeneous Symbols
Fractional Diffusion Equations

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Samuil D. Eidelman, Stepan D. Ivasyshen, Anatoly N. Kochubei
Collection	Operator theory advances and applications
Parution	07/10/2004
Nb. de pages	386
Format	17 x 24
Couverture	Relié
Poids	872g
Intérieur	Noir et Blanc
EAN13	9783764371159