## 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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### References:

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