Advances in Differential Equations

Threshold and strong threshold solutions of a semilinear parabolic equation

Pavol Quittner

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If $p>1+2/n$, then the equation $u_t-\Delta u = u^p, \quad x\in{\mathbb R}^n,\ t>0,$ possesses both positive global solutions and positive solutions which blow up in finite time. We study the large time behavior of radial positive solutions lying on the borderline between global existence and blow-up.

Article information

Adv. Differential Equations, Volume 22, Number 7/8 (2017), 433-456.

Accepted: October 2016
First available in Project Euclid: 4 May 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations 35K57: Reaction-diffusion equations 35B40: Asymptotic behavior of solutions


Quittner, Pavol. Threshold and strong threshold solutions of a semilinear parabolic equation. Adv. Differential Equations 22 (2017), no. 7/8, 433--456.

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