Abstract and Applied Analysis (Jan 2012)

Complicated Asymptotic Behavior of Solutions for Heat Equation in Some Weighted Space

  • Liangwei Wang,
  • Jingxue Yin

DOI
https://doi.org/10.1155/2012/463082
Journal volume & issue
Vol. 2012

Abstract

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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.