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The Energy Method, Stability, and Nonlinear Convection

Author: B Straughan
Publisher: New York, NY : Springer New York, 1992.
Series: Applied mathematical sciences (Springer-Verlag New York Inc.), 91.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is primarily a presentation of nonlinear energy stability obtained in convection problems by means of an integral inequality technique that is referred to as the energy method. While its use was originally based on the kinetic energy of the fluid motion, subsequent work has introduced variations of the classical energy. The new functionals have much in common with the Lyapunov method in partial  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: B Straughan
ISBN: 9781475721942 1475721943
OCLC Number: 851785282
Description: 1 online resource (xii, 243 pages).
Contents: 1. Introduction --
2. Illustration of the Energy Method on Simple Examples and Discussion of Linear Theory --
3. The Navier-Stokes Equations, the Boussinesq Approximation, and the Standard Bénard Problem --
4. Symmetry, Competing Effects, and Coupling Parameters; Multiparameter Eigenvalue Problems; Finite Geometries --
5. Convection Problems in a Half-Space --
6. Generalized Energies and the Lyapunov Method --
7. Geophysical Problems --
8. Surface Tension Driven Convection --
9. Convection in Generalized Fluids --
10. Time Dependent Basic States --
11. Electrohydrodynamic and Magnetohydrodynamic Convection --
12. Ferrohydrodynamic Convection --
13. Convective Instabilities for Reacting Viscous Fluids Far from Equilibrium --
14. Energy Stability and Other Continuum Theories --
Appendix 1. Some Useful Inequalities in Energy Stability Theory --
Appendix 2. Numerical Solution of the Energy Eigenvalue Problem --
A2.1 The Shooting Method --
A2.2 A System: The Viola Eigenvalue Problem --
A2.3 The Compound Matrix Method --
A2.4 Numerical Solution of (4.65), (4.66) Using Compound Matrices --
References.
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), 91.
Responsibility: by Brian Straughan.

Abstract:

This book is primarily a presentation of nonlinear energy stability obtained in convection problems by means of an integral inequality technique that is referred to as the energy method. While its use was originally based on the kinetic energy of the fluid motion, subsequent work has introduced variations of the classical energy. The new functionals have much in common with the Lyapunov method in partial differential equations and standard terminology in the literature would now appear to be generalized energy methods. In this book, the author describes many of the new generalizations and explains why such a generalization was deemed necessary. Additionally, he explains the physical relevance of the problem and indicates the usefulness of an energy technique in this context.

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