Determination of order in fractional diffusion equation
Determination of order in fractional diffusion equation
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发表时间：
2013
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通讯作者：
Yuko Hatano;J. Nakagawa;Sheng-Feng Wang;Masahiro Yamamoto
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作者：
Yuko Hatano;J. Nakagawa;Sheng-Feng Wang;Masahiro Yamamoto
我们证明了通过某一固定空间点的时程重构分数扩散方程中分数阶时间导数阶的公式。证明基于解的渐近性 t ! 0 或 t ！ 1.阶数对于评价异质介质中的扩散异常很重要，特别是，阶数决定了大t下解的衰减率。我们展示了重建公式的数值测试。
We prove formulae of reconstructing the order of fractional derivative in time in the fractional diffusion equation by time history at one fixed spatial point. The proof is based on asymptotics of the solution as t ! 0 or t ! 1. The order is important for evaluating the anomaly of the diffusion in heterogeneous medium, and in particular, the order determines the decay rate of solution for large t. We show numerical tests for our reconstruction formula.