Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
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DOI：
10.2478/s13540-014-0217-x
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发表时间：
2014-09
影响因子：
3
通讯作者：
Zhi-yuan Li;Yuri Luchko;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
Zhi-yuan Li;Yuri Luchko;Masahiro Yamamoto
本文研究有界多维区域上分布阶时间分数阶扩散方程初边值问题解的一些重要性质。特别地，我们研究了当时间变量t → 0和t → +∞时解的渐近性态.利用拉普拉斯变换方法，我们证明了该解随t → +∞而单调衰减.当t → 0时，解的衰减率由（t log（1/t））−1项决定。从而证明了分布阶时间分数阶扩散方程初边值问题解的渐近性态与多项分数阶扩散方程的情形不同.
This article deals with investigation of some important properties of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations in bounded multi-dimensional domains. In particular, we investigate the asymptotic behavior of the solutions as the time variable t → 0 and t → +∞. By the Laplace transform method, we show that the solutions decay logarithmically as t → +∞. As t → 0, the decay rate of the solutions is dominated by the term (t log(1/t))−1. Thus the asymptotic behavior of solutions to the initial-boundary-value problem for the distributed order time-fractional diffusion equations is shown to be different compared to the case of the multi-term fractional diffusion equations.