Applications Of Group Theoretical Methods In Hydrodynamics

Author : V.K. Andreev,O.V. Kaptsov,Vladislav V. Pukhnachev,A.A. Rodionov
Publisher : Springer
Page : 396 pages
File Size : 48,9 Mb
Release : 2013-01-07
Category : Mathematics
ISBN : 9401707464

Get Book

Applications of Group-Theoretical Methods in Hydrodynamics by V.K. Andreev,O.V. Kaptsov,Vladislav V. Pukhnachev,A.A. Rodionov Pdf

It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in variant and partially invariant solutions to the equations of hydrodynamics.

Author : V.K. Andreev,O.V. Kaptsov,Vladislav V. Pukhnachev,A.A. Rodionov
Publisher : Springer Science & Business Media
Page : 966 pages
File Size : 46,6 Mb
Release : 1998-10-31
Category : Mathematics
ISBN : 0792352157

Get Book

Applications of Group-Theoretical Methods in Hydrodynamics by V.K. Andreev,O.V. Kaptsov,Vladislav V. Pukhnachev,A.A. Rodionov Pdf

It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in variant and partially invariant solutions to the equations of hydrodynamics.

Author : V.K. Andreev,O.V. Kaptsov,Vladislav V. Pukhnachev,A.A. Rodionov
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 46,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401707459

Get Book

Applications of Group-Theoretical Methods in Hydrodynamics by V.K. Andreev,O.V. Kaptsov,Vladislav V. Pukhnachev,A.A. Rodionov Pdf

It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in variant and partially invariant solutions to the equations of hydrodynamics.

Author : Olga S. Rozanova
Publisher : Nova Publishers
Page : 260 pages
File Size : 40,6 Mb
Release : 2006
Category : Science
ISBN : 1594543070

Get Book

Analytical Approaches to Multidimensional Balance Laws by Olga S. Rozanova Pdf

It is difficult to overestimate the importance of mathematical investigation of balance laws. They arise in many areas of physics, mechanics, chemistry, biology, social sciences. In this collective book we concentrate in particular on the equations of continuous medium and related to them. As a rule, they are very complicated in their primitive form. An important feature of such equations is a possible formation of singularities even in initially smooth solution within a finite time. The structure of the singularities can be very complex. A natural step in the approach to this problem is the transition, despite the three-dimensionality of our world, to spatially one-dimensional model. Significant progress has been achieved in this direction. Unfortunately, the methods of the one-dimensional theory, as usual, cannot be adapted to a case of many spatial variables. However, there are many attempts to deal with multidimensional problems. We would like to present some of them. All of the papers are written by outstanding experts, representing various schools in mathematics and mechanics. Each paper is organised as follows: it contains an elementary (as far as it is possible) introduction to a problem, a brief review of previously published results, and then original results of the authors are presented.

Author : Vladimir Gordin
Publisher : CRC Press
Page : 812 pages
File Size : 42,9 Mb
Release : 2000-09-20
Category : Mathematics
ISBN : 9781482287417

Get Book

Mathematical Problems and Methods of Hydrodynamic Weather Forecasting by Vladimir Gordin Pdf

The material provides an historical background to forecasting developments as well as introducing recent advances. The book will be of interest to both mathematicians and physicians, the topics covered include equations of dynamical meteorology, first integrals, non-linear stability, well-posedness of boundary problems, non-smooth solutions, parame

Author : Brian J. Cantwell
Publisher : Cambridge University Press
Page : 655 pages
File Size : 41,8 Mb
Release : 2002-09-26
Category : Mathematics
ISBN : 9781009074452

Get Book

Introduction to Symmetry Analysis by Brian J. Cantwell Pdf

Author : Andrei D. Polyanin,Valentin F. Zaitsev
Publisher : CRC Press
Page : 1878 pages
File Size : 48,9 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781420087246

Get Book

Handbook of Nonlinear Partial Differential Equations, Second Edition by Andrei D. Polyanin,Valentin F. Zaitsev Pdf

New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.

Author : Andrei D. Polyanin,Valentin F. Zaitsev
Publisher : CRC Press
Page : 835 pages
File Size : 52,8 Mb
Release : 2003-10-29
Category : Mathematics
ISBN : 9780203489659

Get Book

Handbook of Nonlinear Partial Differential Equations by Andrei D. Polyanin,Valentin F. Zaitsev Pdf

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types,

Author : Darya Apushkinskaya,Alexander I. Nazarov
Publisher : American Mathematical Society
Page : 282 pages
File Size : 48,7 Mb
Release : 2014-08-22
Category : Mathematics
ISBN : 9781470415518

Get Book

Proceedings of the St. Petersburg Mathematical Society, Volume XV by Darya Apushkinskaya,Alexander I. Nazarov Pdf

This book presents the proceedings of the international workshop, "Advances in Mathematical Analysis of Partial Differential Equations" held at the Institut Mittag-Leffler, Stockholm, Sweden, July 9-13, 2012, dedicated to the memory of the outstanding Russian mathematician Olga A. Ladyzhenskaya. The volume contains papers that engage a wide set of modern topics in the theory of linear and nonlinear partial differential equations and applications, including variational and free boundary problems, mathematical problems of hydrodynamics, and magneto-geostrophic equations.

Author : Victor A. Galaktionov,Sergey R. Svirshchevskii
Publisher : CRC Press
Page : 530 pages
File Size : 40,5 Mb
Release : 2006-11-02
Category : Mathematics
ISBN : 9781420011623

Get Book

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics by Victor A. Galaktionov,Sergey R. Svirshchevskii Pdf

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book

Author : Armand Wirgin
Publisher : World Scientific
Page : 301 pages
File Size : 45,9 Mb
Release : 2002
Category : Science
ISBN : 9789812382641

Get Book

Acoustics, Mechanics, and the Related Topics of Mathematical Analysis by Armand Wirgin Pdf

At head of title: Proceedings of the International Conference to celebrate Robert P. Gilbert's 70th birthday.

Author : Armand Wirgin
Publisher : World Scientific
Page : 300 pages
File Size : 50,6 Mb
Release : 2003-01-13
Category : Mathematics
ISBN : 9789814486743

Get Book

Acoustics, Mechanics, and the Related Topics of Mathematical Analysis by Armand Wirgin Pdf

This book concerns the mathematical analysis — modeling physical concepts, existence, uniqueness, stability, asymptotics, computational schemes, etc. — involved in predicting complex mechanical/acoustical behavior/response and identifying or optimizing mechanical/acoustical systems giving rise to phenomena that are either observed or aimed at. The forward problems consist in solving generally coupled, nonlinear systems of integral or partial (integer or fractional) differential equations with nonconstant coefficients. The identification/optimization of the latter, of the driving terms and/or of the boundary conditions, all of which are often affected by random perturbations, forms the class of related inverse or control problems. Contents:Imaging Methods in Random Media (J Berryman et al.)Resonances of an Elastic Plate in a Duct, in the Presence of a Uniform Flow (A S B-B Dhia & J-F Mercier)First Order Asymptotic Modelling of a Nuclear Waste Repository (A Bourgeat et al.)Recovery of the Poroelastic Parameters of Cancellous Bone Using Low Frequency Acoustic Interrogation (J L Buchanan et al.)Trapping Regions for Discontinuously Coupled Dynamic Systems (S Carl & J W Jerome)Differential Calculi (R Carroll)Homogenizing a Flow of an Incompressible Inviscid Fluid Through an Elastic Porous Media (T Clopeau & A Mickelic)On the Hardy Spaces of Harmonic and Monogenic Functions in the Unit Ball of RM+1 (R Delanghe)A Model for Porous Ductile Viscoplastic Solids including Void Shape Effects (L Flandi & J-B Leblond)Acoustic Wave Propagation in a Composite of Two Different Poroelastic Materials with a very Rough Periodic Interface: a Homogenization Approach (R Gilbert & M-J Ou)A Survey of Pointwise Interpolation Inequalities for Integer and Fractional Derivatives (V Maz'ya & T Shaposhnikova)Recent Progress in the Theoretical and Numerical Modelling of Thin-Layer Flow (L Schwartz)and other papers Readership: Researchers, academics and graduate students in the fields of analysis and differential equations, applied mathematics, mechanics and mathematical physics. Keywords:Analysis;Integral and Partial Differential Equations;Solid and Fluid Mechanics

Author : E. Stiefel,A. Fässler
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203957

Get Book

Group Theoretical Methods and Their Applications by E. Stiefel,A. Fässler Pdf

X system Ib-TEX. I wish to thank her for the beautiful work and the numerous discussions on the contents of this book. I am indebted to Peter Fassler, Neu-Technikum Buchs, Switzerland, for drafting the figures, to my students Kurt Rothermann and Stefan Strahl for computer enhancing and labeling the graphics, to Pascal Felder and Markus Wittwer for a simulation program that generated the figures in the stochastics sections. My thanks go to my new colleague at work, Daniel Neuenschwander, for the inspiring discussions related to the section in stochastics and for reading the manuscript to it. I am also grateful to Dacfey Dzung for reading the whole manuscript. Thanks go especially to Professor \Valter Gander of ETH, Zurich, who at the finishing stage and as an expert of 'JEXgenerously invested numerous hours to assist us in solving software as well as hardware problems; thanks go also to Martin Muller, Ingenieurschule Biel, who made the final layout of this book on the NeXT computer. Thanks are also due to Helmut Kopka of the Max Planck Institute, for solving software problems, and to Professor Burchard Kaup of the Uni versity of Fribourg, Switzerland for adding some useful software; also to Birkhauser Boston Inc. for the pleasant co-operation. Finally, let me be reminiscent of Professor E. Stiefel (deceased 1978) with whom I had many interesting discussions and true co-operation when writing the book in German.

Author : Andrei D. Polyanin,Alexander V. Manzhirov
Publisher : CRC Press
Page : 1542 pages
File Size : 52,8 Mb
Release : 2006-11-27
Category : Mathematics
ISBN : 9781420010510

Get Book

Handbook of Mathematics for Engineers and Scientists by Andrei D. Polyanin,Alexander V. Manzhirov Pdf

The Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgr

Author : Mohamed El-Amin
Publisher : BoD – Books on Demand
Page : 642 pages
File Size : 55,5 Mb
Release : 2011-02-21
Category : Science
ISBN : 9789533073330

Get Book

Advanced Topics in Mass Transfer by Mohamed El-Amin Pdf

This book introduces a number of selected advanced topics in mass transfer phenomenon and covers its theoretical, numerical, modeling and experimental aspects. The 26 chapters of this book are divided into five parts. The first is devoted to the study of some problems of mass transfer in microchannels, turbulence, waves and plasma, while chapters regarding mass transfer with hydro-, magnetohydro- and electro- dynamics are collected in the second part. The third part deals with mass transfer in food, such as rice, cheese, fruits and vegetables, and the fourth focuses on mass transfer in some large-scale applications such as geomorphologic studies. The last part introduces several issues of combined heat and mass transfer phenomena. The book can be considered as a rich reference for researchers and engineers working in the field of mass transfer and its related topics.