Explosive Instabilities in Mechanics /
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 mech...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
1998.
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (ix, 196 pages) |
| ISBN: | 9783642588075 (electronic bk.) 3642588077 (electronic bk.) |