© 1992

The Energy Method, Stability, and Nonlinear Convection


Part of the Applied Mathematical Sciences book series (AMS, volume 91)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Brian Straughan
    Pages 1-2
  3. Brian Straughan
    Pages 75-81
  4. Brian Straughan
    Pages 82-107
  5. Brian Straughan
    Pages 108-131
  6. Brian Straughan
    Pages 132-144
  7. Brian Straughan
    Pages 145-153
  8. Brian Straughan
    Pages 154-160
  9. Brian Straughan
    Pages 176-189
  10. Brian Straughan
    Pages 204-206
  11. Back Matter
    Pages 207-243

About this book


The writing of this book was begun during the academic year 1984-1985 while I was a visiting Associate Professor at the University of Wyoming. I am extremely grateful to the people there for their help, in particular to Dick Ewing, Jack George and Robert Gunn, and to Ken Gross, who is now at the University of Vermont. A major part of the first draft of this book was written while I was a visiting Professor at the University of South Carolina during the academic year 1988-1989. I am indebted to the people there for their help, in one way or another, particularly to Ron DeVore, Steve Dilworth, Bob Sharpley, Dave Walker, and especially to the chairman of the Mathematics Department at the University of South Carolina, Colin Bennett. I also wish to express my sincere gratitude to Ray Ogden and Profes­ sor I.N. Sneddon, F.R.S., both of Glasgow University, for their help over a number of years. I also wish to record my thanks to Ron Hills and Paul Roberts, F.R.S., for giving me a copy of their paper on the Boussinesq ap­ proximation prior to publication and for allowing me to describe their work here. I should like to thank my Ph.D. student Geoff McKay for spotting several errors and misprints in an early draft. Finally, I am very grateful to an anonymous reviewer for several pertinent suggestions regarding the energy-Casimir method.


convection differential equation energy partial differential equation quality stability stability theory

Authors and affiliations

  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK

Bibliographic information

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From the reviews of the second edition:

"This application-oriented book is a revised edition … more definitions, new interpretations and new results are included, some chapters are enlarged, 6 chapters are added. … the presentation is very clear, making the book useful to undergraduate and graduate students in applied mathematics too. … The main text and the very rich list of references reflect the interests and results of the author and his collaborators. The book makes a good contribution to the literature on stability of fluid flows … ." (Adelina Georgescu, Mathematical Reviews, 2004i)