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- W1987680771 abstract "We examine the behavior of positive bounded, localized solutions of semilinear parabolic equations $u_t=Delta u+f(u)$ on $mathbb{R}^N$. Here $fin C^1$, $f(0)=0$, and a localized solution refers to a solution $u(x,t)$ which decays to 0 as $xtoinfty$ uniformly with respect to $t>0$. In all previously known examples, bounded, localized solutions are convergent or at least quasi-convergent in the sense that all their limit profiles as $ttoinfty$ are steady states. If $N=1$, then all positive bounded, localized solutions are quasi-convergent. We show that such a general conclusion is not valid if $Nge 3$, even if the solutions in question are radially symmetric. Specifically, we give examples of positive bounded, localized solutions whose $omega$-limit set is infinite and contains only one equilibrium." @default.
- W1987680771 created "2016-06-24" @default.
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- W1987680771 date "2014-01-01" @default.
- W1987680771 modified "2023-10-16" @default.
- W1987680771 title "Localized Solutions of a Semilinear Parabolic Equation with a Recurrent Nonstationary Asymptotics" @default.
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- W1987680771 doi "https://doi.org/10.1137/140958566" @default.
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