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The decay of global solutions of a semilinear heat equation

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  • 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.
    Mathematics Subject Classification: Primary: 35K55, 35K57, 35B40; Secondary: 35B45.


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