An inverse problem for a one-dimensional time-fractional diffusion problem
An inverse problem for a one-dimensional time-fractional diffusion problem
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DOI：
10.1088/0266-5611/28/7/075010
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发表时间：
2012-06
期刊：
影响因子：
2.1
通讯作者：
Bangti Jin;W. Rundell
中科院分区：
文献类型：
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作者：
Bangti Jin;W. Rundell
我们研究了一个反问题，恢复一个空间变化的潜力项在一维时间分数扩散方程的流量测量在一个单一的固定时间对应于一组给定的输入源。在输入源的集合构成L2（0，1）中的完备基的条件下，证明了势的唯一可辨识性，即在一端的通量和净通量两种情况下.本文提出了一种拟牛顿型算法，从有限数据中有效而精确地重建系数，并讨论了雅可比矩阵的内射性。精确和噪声数据的数值结果。
We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique identifiability of the potential is shown for two cases, i.e. the flux at one end and the net flux, provided that the set of input sources forms a complete basis in L2(0, 1). An algorithm of the quasi-Newton type is proposed for the efficient and accurate reconstruction of the coefficient from finite data, and the injectivity of the Jacobian is discussed. Numerical results for both exact and noisy data are presented.