Explosive Instabilities In Mechanics

This book deals with blow-up of 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, then concentrates on mechanics. 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, stressing how these equations arise in mechanics, e.g. in combustion theory. Further topics are chemotaxis in mathematical biology, change of type, from hyperbolic to elliptic, instability in soils, instability in sea ice dynamics, instability in pressure-dependent viscosity flow, and energy growth in parallel shear flows. It addresses graduate students and researchers in mechanics.