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

Liangwei Wang and Jingxue Yin

Abstract and Applied Analysis, 2012, vol. 2012, 1-15

Abstract:

We investigate the asymptotic behavior of solutions for the heat equation in the weighted space ð ‘Œ 𠜎 0 ( â„ ð ‘ ) ≡ { 𠜑 ∈ ð ¶ ( â„ ð ‘ ) ∶ l i m | ð ‘¥ | → ∞ ( 1 + | ð ‘¥ | 2 ) − 𠜎 / 2 𠜑 ( ð ‘¥ ) = 0 } . Exactly, we find that the unbounded function space ð ‘Œ 𠜎 0 ( â„ ð ‘ ) with 0 < 𠜎 < ð ‘ can provide a setting where complexity occurs in the asymptotic behavior of solutions for the heat equation.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:463082

DOI: 10.1155/2012/463082

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