Recovery of multiple parameters in subdiffusion from one lateral boundary measurement
Recovery of multiple parameters in subdiffusion from one lateral boundary measurement
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DOI：
10.1088/1361-6420/acef50
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发表时间：
2023-07
期刊：
影响因子：
2.1
通讯作者：
Siyu Cen;Bangti Jin;Yikan Liu;Zhi Zhou
中科院分区：
文献类型：
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作者：
Siyu Cen;Bangti Jin;Yikan Liu;Zhi Zhou
这项工作涉及的数值恢复多个参数同时在亚扩散模型从一个单一的横向测量的边界的一部分，而在一个不完全已知的介质。我们证明了一个相当一般的边界激励对应的边界测量唯一确定的阶的分数阶导数和多边形支持的扩散系数，不知道初始条件或源。的唯一性分析进一步启发了发展一个强大的数值算法恢复分数阶和扩散系数。该算法结合了小时间渐近展开、解的解析延拓和水平集方法。我们提出了广泛的数值实验来说明同时恢复的可行性。此外，我们讨论了恢复一般的扩散和潜在的系数从一个单一的部分边界测量的唯一性，当边界激发更专业。
This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary measurement corresponding to a fairly general boundary excitation uniquely determines the order of the fractional derivative and the polygonal support of the diffusion coefficient, without knowing either the initial condition or the source. The uniqueness analysis further inspires the development of a robust numerical algorithm for recovering the fractional order and diffusion coefficient. The proposed algorithm combines small-time asymptotic expansion, analytic continuation of the solution and the level set method. We present extensive numerical experiments to illustrate the feasibility of the simultaneous recovery. In addition, we discuss the uniqueness of recovering general diffusion and potential coefficients from one single partial boundary measurement, when the boundary excitation is more specialized.