Mathematical Methods using Mathematica

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Michael Růžička

This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

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Michael Reed, Barry Simon

"This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations." --Publisher description.

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Michel Remoissenet

Written for an interdisciplinary readership of physicists, engineers, and chemists, this book is a practical guide to the fascinating world of solitons. These waves of large amplitude propagate over long distances without dispersing and therefore show one of the most striking aspects of nonlinearity. The author addresses students, practitioners, and researchers, approaching the subject from the standpoint of applications in optics, hydrodynamics, and electrical and chemical engineering. The book also encourages the readers to perform their own experiments. Since the printing of the second edition of this book, there has been a large growth in the literature on nonlinear waves and so has the wide applicability of the subject to the physical, chemical and biological sciences. Accordingly, this third edition has been thoroughly revised. Some of the topics are brought up to date with pertinent references. Furthermore, the book now includes a completely new chapter on solitary waves in diffuse systems.

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Rouslan L. Stratonovich

This book gives the first detailed and coherent treatment of a young and exciting branch of statistical physics. The author presents a new common theoretical framework describing both linear and nonlinear nonequilibrium thermodynamics. This first of two volumes is concerned largely with the derivation and applications of various types of fluctuation-dissipation theorems. Both theoretical physicists and applied scientists will find this material of interest since the theoretical treatment is supported by numerous illustrative examples and application of the general result to a variety of electrical, thermal, mechanical and chemical systems.