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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.

MSC:

35K05 Heat equation
35B40 Asymptotic behavior of solutions to PDEs
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