Explosive Instabilities in Mechanics
By: by Brian Straughan
Publisher: Springer Berlin Heidelberg
Published: 1998
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 196
ISBN-13: 9783642637407; 9783642588075
Subjects: Mechanics; Physics; Applied Mechanics
Description: 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.
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Table of contents: title: Introduction; title: Analysis of a First-Order System; title: Singularities for Classical Fluid Equations; title: Catastrophic Behaviour in Other Nonlinear Fluid Theories; title: Blow-Up in Volterra Equations; title: Chemotaxis; title: Change of Type; title: Rapid Energy Growth in Parallel Flows; title: Bibliography; title: Index.