Applications of Group-Theoretical Methods in Hydrodynamics / Edition 1

Applications of Group-Theoretical Methods in Hydrodynamics / Edition 1

by V.K. Andreev, O.V. Kaptsov, Vladislav V. Pukhnachev, A.A. Rodionov
     
 

ISBN-10: 0792352157

ISBN-13: 9780792352150

Pub. Date: 10/31/1998

Publisher: Springer Netherlands

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…  See more details below

Overview

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.

Read More

Product Details

ISBN-13:
9780792352150
Publisher:
Springer Netherlands
Publication date:
10/31/1998
Series:
Mathematics and Its Applications (closed) Series, #450
Edition description:
1998
Pages:
408
Product dimensions:
6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Foreword to the English Translation
Preface
Ch. 1Group-Theoretic Classification of the Equations of Motion of a Homogeneous or Inhomogeneous Inviscid Fluid in the Presence of Planar and Rotational Symmetry
Ch. 2Exact Solutions to the Nonstationary Euler Equations in the Presence of Planar and Rotational Symmetry
Ch. 3Nonlinear Diffusion Equations and Invariant Manifolds
Ch. 4The Method of Defining Equations
Ch. 5Stationary Vortex Structures in an Ideal Fluid
Ch. 6Group-Theoretic Properties of the Equations of Motion for a Viscous Heat Conducting Liquid
Ch. 7Exact Solutions to the Equations of Dynamics for a Viscous Liquid
Bibliography
Subject Index

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >