Single-point blowup for nonlocal parabolic problems

The formation of shear bands in materials has important implications to a v ariety of physical processes. These bands are observed in very thin zones a nd are generally regarded as a precursor to material failure. Shear band fo rmation is caused by the heat generated in regions with highest strain rate . With insufficient time for diffusion of this heat, a localized thermal so ftening of the material occurs which enhances plastic flow in a thin zone. This adiabatic strain localization can be modelled as nonlinear thermally-a ctivated reaction-diffusion equations. This leads to a class of nonlocal pa rabolic problems and their associated time-independent steady-state counter parts. A discussion of the models and an analysis of the problems will be p resented. (C) 1999 Elsevier Science B.V. All rights reserved.