Explosive Instabilities in Mechanics - Softcover

Straughan, Brian

Softcover

ISBN 10: 364263740X ISBN 13: 9783642637407

Publisher: Springer, 2012

Synopsis

This book deals with explosive instabilities in mechanics, deriving a solution to a system of PDEs that arise in practical situations. It begins with a relatively simple account of blow-up in systems of interaction-diffusion equations. Among the topics presented are: classical fluid equations, catastrophic behavior in nonlinear fluid theories, blow-up in Volterra equations, and rapid energy growth in parallel flows.

About this title

Review:

From the reviews
"... this book contains a clear account of exciting works in various parts of science, concentrating on blow-up solutions of systems of partial differential equations."
(J. Cugnon in: Physicalia)

From the Back Cover:

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.

About this edition

• Publisher: Springer
• Publication date: 2012
• ISBN 10: 364263740X
• ISBN 13: 9783642637407
• Binding: Paperback
• Number of pages: 206