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Sinopsis
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.
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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.
Reseña del editor
This book presents applications of group analysis of differential equations to various models used in hydrodynamics. It contains many new examples of exact solutions to the boundary value problems for the Euler and Navier-Stokes equations. These solutions describe vortex structures in an inviscid fluid, Marangoni boundary layers, thermal gravity convection and other interesting effects. Moreover, the book provides a new method for finding solutions of nonlinear partial differential equations, which is illustrated by a number of examples, including equations for flows of a compressible ideal fluid in two and three dimensions. The work is reasonably self-contained and supplemented by examples of direct physical importance.
Audience: This volume will be of interest to postgraduate students and researchers whose work involves partial differential equations, Lie groups, the mathematics of fluids, mathematical physics or fluid mechanics.
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Applications Of Group-theoretical Methods In Hydrodynamics
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Applications of Group-Theoretical Methods in Hydrodynamics
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Gebunden. Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 t. Nº de ref. del artículo: 5968572
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Applications of Group-Theoretical Methods in Hydrodynamics (Mathematics and Its Applications, 450)
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Applications of Group-Theoretical Methods in Hydrodynamics
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Springer Netherlands, Springer Netherlands, 1998
ISBN 10: 0792352157
ISBN 13: 9780792352150
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Buch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9780792352150
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Applications of Group-Theoretical Methods in Hydrodynamics
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Springer Netherlands, Springer Netherlands Okt 1998, 1998
ISBN 10: 0792352157
ISBN 13: 9780792352150
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Buch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 412 pp. Englisch. Nº de ref. del artículo: 9780792352150
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Applications of Group-Theoretical Methods in Hydrodynamics (Mathematics and Its Applications, 450)
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Applications of Group-Theoretical Methods in Hydrodynamics
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Springer Netherlands Okt 1998, 1998
ISBN 10: 0792352157
ISBN 13: 9780792352150
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Librería: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Alemania
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 412 pp. Englisch. Nº de ref. del artículo: 9780792352150
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Applications of Group-Theoretical Methods in Hydrodynamics (Mathematics and Its Applications (450))
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