具有对合的多项时间分数演化方程的反问题

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2021-11-18 DOI:10.1080/17415977.2021.2000606

Asim Ilyas, S. Malik, Summaya Saif

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引用次数: 7

摘要

本文主要考虑具有对合项的多项时间分数演化方程的两个逆源问题，插值热和波方程。分数阶导数是卡普托意义上的定义。在Hadamard的意义上，isp被证明是病态的。在第一个ISP中，从给定的某一时刻的过指定数据中恢复空间相关的源项，而在第二个ISP中，当给定整数型的过指定条件时，考虑源项的时间相关分量的确定。利用傅里叶方法构造了isp的解。解的时变分量用多项Mittag-Leffler函数表示。在一定条件下，证明了多项时间分数进化方程的ISPs解是经典解。此外，还制定了一些具体的例子来说明isp的所得结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Inverse problems for a multi-term time fractional evolution equation with an involution

This paper focuses on considering two inverse source problems (ISPs) for a multi-term time-fractional evolution equation with an involution term, interpolating the heat and wave equations. The fractional derivatives are defined in Caputo's sense. The ISPs are proved to be ill-posed in the sense of Hadamard. Recovering a space dependent source term from over-specified data given at some time constitute the first ISP, while in the second ISP determination of a time dependent component of the source term is considered when over-specified condition of integral type is given. The solution of ISPs are constructed by using Fourier's method. The time-dependent components of the solutions are presented in terms of the multinomial Mittag-Leffler function. Under certain conditions, the solutions of ISPs for the multi-term time-fractional evolution equation are shown to be classical solutions. In addition, some particular examples are formulated to illustrate the obtained results for the ISPs.

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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.