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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:
35K55Nonlinear parabolic equations
35-02Research monographs (partial differential equations)
35K45Systems of second-order parabolic equations, initial value problems
35B40Asymptotic behavior of solutions of PDE
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