Complicated Asymptotic Behavior of Solutions for Heat Equation in Some Weighted Space - Liangwei Wang; Jingxue Yin (Abstract and Applied Analysis)
We investigate the asymptotic behavior of solutions for the heat equation in the weighted space Y0σ(ℝN)≡{φ∈C(ℝN):lim |x|→∞(1+|x|2)-σ/2φ(x)=0}. Exactly, we find that the unbounded function space Y0σ(ℝN) with 0<σ<N can provide a setting where complexity occurs in the asymptotic behavior of solutions for the heat equation.