Differential and Integral Equations

Life span of positive solutions for a semilinear heat equation with non-decaying initial data

Masaki Yamaguchi and Yusuke Yamauchi

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Abstract

We consider an estimate of the life span of solutions on a semilinear heat equation. In one dimension, we show that the life span may be estimated from above in terms of the average of two limits as $x\to\pm\infty$ of the initial data. In general dimensions, under some monotonicity conditions for initial data, an explicit representation of the uniform norm of the life span of solutions is obtained.

Article information

Source
Differential Integral Equations, Volume 23, Number 11/12 (2010), 1151-1157.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019078

Mathematical Reviews number (MathSciNet)
MR2742483

Zentralblatt MATH identifier
1240.35218

Subjects
Primary: 35K05: Heat equation 35K57: Reaction-diffusion equations 35K58: Semilinear parabolic equations 35B44: Blow-up

Citation

Yamaguchi, Masaki; Yamauchi, Yusuke. Life span of positive solutions for a semilinear heat equation with non-decaying initial data. Differential Integral Equations 23 (2010), no. 11/12, 1151--1157. https://projecteuclid.org/euclid.die/1356019078


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