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**Complicated asymptotic behavior of solutions for heat equation in some weighted space.**
*(English)*
Zbl 1247.35054

Summary: We investigate the asymptotic behavior of solutions for the heat equation in the weighted space \(Y^\sigma_0(\mathbb R^N) \equiv \{\varphi \in C(\mathbb R^N) : \lim_{|x| \rightarrow \infty}(1 + |x|^2)^{-\sigma/2} \varphi(x) = 0\}\). Exactly, we find that the unbounded function space \(Y^\sigma_0(\mathbb R^N)\) with \(0 < \sigma < N\) can provide a setting where complexity occurs in the asymptotic behavior of solutions for the heat equation.

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\textit{L. Wang} and \textit{J. Yin}, Abstr. Appl. Anal. 2012, Article ID 463082, 15 p. (2012; Zbl 1247.35054)

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