Distributions in the physical and engineering sciences. Volume 3. Random and anomalous fractional dynamics in continuous media
type: Item
instance of: scholarly article
title: Distributions in the physical and engineering sciences. Volume 3. Random and anomalous fractional dynamics in continuous media
zbMATH Open document ID: 1403.46001
DOI: 10.1007/978-3-319-92586-8
author: Alexander I. Saichev
author: Wojbor A. Woyczyński
published in: Applied and Numerical Harmonic Analysis
publication date: 2018-06-29T00:00:00Z
review text: This book, which could be renamed ``Generalized functions for physicists and engineers'', deals with stochastic processes and fractional dynamics. This is a book for applied mathematicians, as illustrated by the fact that there is neither filtration nor measure or the like in the expansion related to stochastic differential equations, for instance. Here, we are in Laurent Schwartz's tradition. The book is composed of two parts which deal with random dynamics on the one hand and anomalous fractional dynamics on the other hand. Contents of Part I: random distribution, random field, Burger turbulence, randomly moving media. Contents of Part II: Lévy processes, fractional dynamics in continuous media, nonlinear and multiscale fractional dynamics in continuous media. All the modeling developments are accompanied by illustrative practical examples which support the theory. The book intends to fill in the gap between no mathematics on the one hand, and applied mathematics on the other hand, and it works well. The defect of the book lies in its reference list which should be a small bibliography, however, some striking works on the topic are missing. But I agree that, if I use the Einstein special relativistic equation somewhere, I do not have to mention any reference. Editorial remark: Volumes 1 and 2 have been reviewed in (1997; Zbl 0880.46028) and (2013; Zbl 1283.46001), respectively.
Mathematics Subject Classification ID: 46-01
Mathematics Subject Classification ID: 46F99
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 37-01
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 82C99
zbMATH DE Number: 6897911
zbMATH Keywords: potential theory
zbMATH Keywords: elliptic equations
zbMATH Keywords: parabolic equations
zbMATH Keywords: hyperbolic equations
zbMATH Keywords: nonlinear partial differential equations
zbMATH Keywords: conservation laws
zbMATH Keywords: flows in porous media
reviewed by: Guy Jumarie
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-92586-8
OpenAlex ID: W4237702663
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description: scientific article; zbMATH DE number 6897911