Complicated asymptotic behavior of solutions for heat equation in some weighted space
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.
scientific article; zbMATH DE number 6078739
scientific article