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January  2008, 21(1): 307-318. doi: 10.3934/dcds.2008.21.307

The decay of global solutions of a semilinear heat equation

Pavol Quittner 1,

1. 

Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovak Republic

Received  December 2006 Revised  August 2007 Published  February 2008

We are interested in the time decay estimates of global solutions of the semilinear parabolic equation $u_t= \Delta u+|u|^{p-1}u$ in $\R^N\times\R^+$, where $p>1$. We find several new sufficient and/or necessary conditions guaranteeing that the solution for $t$ large behaves like the solution of the linear heat equation or has the self-similar decay. We are particularly interested in the behaviour of threshold solutions lying on the borderline between global existence and blow-up.
Keywords: blow-up., Semilinear heat equation, decay of global solutions.
Mathematics Subject Classification: Primary: 35K55, 35K57, 35B40; Secondary: 35B4.
Citation: Pavol Quittner. The decay of global solutions of a semilinear heat equation. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 307-318. doi: 10.3934/dcds.2008.21.307
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