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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.
MSC:
35K58Semilinear parabolic equations
35B44Blow-up (PDE)
35K15Second order parabolic equations, initial value problems
References:
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[7]Seki, Y.; Umeda, N.; Suzuki, R.: Blow-up directions for quasilinear parabolic equations, Proc. roy. Soc. Edinburgh sect. A 138, 379-405 (2008) · Zbl 1167.35393 · doi:10.1017/S0308210506000801
[8]Yamaguchi, M.; Yamauchi, Y.: Life span of positive solutions for a semilinear heat equation with non-decaying initial data, Differential integral equations 23, 1151-1157 (2010)