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Explosive Instabilities in Mechanics

  • Brian Straughan

Table of contents

  1. Front Matter
    Pages I-IX
  2. Brian Straughan
    Pages 1-31
  3. Brian Straughan
    Pages 33-61
  4. Brian Straughan
    Pages 63-79
  5. Brian Straughan
    Pages 119-129
  6. Brian Straughan
    Pages 131-142
  7. Brian Straughan
    Pages 143-154
  8. Brian Straughan
    Pages 155-178
  9. Back Matter
    Pages 179-197

About this book

Introduction

This book deals with blow-up, or at least very rapid growth, of a solution to a system of partial differential equations that arise in practical physics situations. It begins with a relatively simple account of blow-up in systems of interaction-diffusion equations.
Then the book concentrates on mechanics applications. In particular it deals with the Euler equations, Navier--Stokes equations, models for glacier physics, Korteweg--de-Vries equations, and ferro-hydrodynamics. Blow-up is treated in Volterra equations, too, stressing how these equations arise in mechanics, e.g. in combustion theory. The novel topic of chemotaxis in mathematical biology is also presented. There is a chapter on change of type, from hyperbolic to elliptic, addressing three new and important applications: instability in soils, instability in sea ice dynamics, and also instability in pressure-dependent viscosity flow. Finally, the book includes an exposition of exciting work, very recent and on-going, dealing with rapid energy growth in parallel shear flows.
The book addresses graduate students as well as researchers in mechanics and applied mathematics.

Keywords

dynamics finite element method finite elements instability mechanics stability stress

Authors and affiliations

  • Brian Straughan
    • 1
  1. 1.Department of MathematicsUniversity of GlasgowGlasgowScotland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58807-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63740-7
  • Online ISBN 978-3-642-58807-5
  • Buy this book on publisher's site