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Life span of positive solutions for a semilinear heat equation with general non-decaying initial data. (English) Zbl 1215.35091
Summary: We prove upper bounds on the life span of positive solutions for a semilinear heat equation. For non-decaying initial data, it is well known that the solutions blow up in finite time. We give two types of estimates of the life span in terms of the limiting values of the initial data in space.

35K58 Semilinear parabolic equations
35B44 Blow-up in context of PDEs
35K15 Initial value problems for second-order parabolic equations
Full Text: DOI
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