一般多维域上变阶分数阶偏微分方程的唯一辨识

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Inverse Problems in Science and Engineering Pub Date : 2020-11-20 DOI:10.1080/17415977.2020.1849182

Xiangcheng Zheng, Hong Wang

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引用次数: 6

摘要

摘要:我们证明了在一般多维域上具有变扩散张量的二尺度移动-不移动变阶时间-分数阶偏微分方程的变量阶的唯一确定，并在足够小的时间间隔内观察到任意小空间域上的未知解。已证明的定理为应该在哪里进行测量提供了指导，并确保通过这些观察，识别的唯一性在理论上得到了保证。

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Uniquely identifying the variable order of time-fractional partial differential equations on general multi-dimensional domains

ABSTRACT We proved the unique determination of the variable order in a two-scale mobile–immobile variable-order time-fractional partial differential equation with a variable diffusivity tensor imposed on a general multi-dimensional domain, with the observations of the unknown solutions on any arbitrarily small spatial domain over a sufficiently small time interval. The proved theorem provides a guidance where the measurements should be performed and ensures that with these observations the uniqueness of the identification is theoretically guaranteed.

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来源期刊

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.