Distributions in the physical and engineering sciences. Volume 3. Random and anomalous fractional dynamics in continuous media
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.
nonlinear partial differential equations
scientific article; zbMATH DE number 6897911