The problem of blow-up in nonlinear parabolic equations (Q1599901)

This survey discusses nonlinear parabolic equations which possess solutions that become unbounded (blow up) in finite time. The authors propose six basic questions: (1)~Does blow-up occur? (2)~When? (3)~Where? (4)~How? (5)~What happens later? (6)~How to compute it numerically? Some answers to these questions are reviewed with emphasis on authors' own contributions. Particular attention is given to the very interesting fifth question, namely, to the study of continuation after blow-up.