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The problem of blow-up in nonlinear parabolic equations. (English) Zbl 1010.35057
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.

MSC:
35K55 Nonlinear parabolic equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35K45 Initial value problems for second-order parabolic systems
35B40 Asymptotic behavior of solutions to PDEs
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