多期时间分式波方程的阶次和势的唯一反演

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-09-28 DOI:10.1016/j.aml.2024.109319

Xuyan Jiang, Zhiyuan Li

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引用次数: 0

摘要

本文研究了确定多期时间分式波方程的阶次和势函数的逆问题。通过分析多元 Mittag-Leffler 函数的渐近行为，我们证明了利用内域测量数据反演阶次和势项的唯一性。文章还提供了数值模拟，展示了如何处理噪声数据并通过提霍诺夫正则化重建方程参数。

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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Unique inversion of orders and potential for multi-term time fractional wave equations

The paper investigates an inverse problem of determining the orders and potential function of multi-term time fractional wave equations. By analyzing the asymptotic behavior of the multivariate Mittag–Leffler function, we show the uniqueness of the inverting the orders and potential term using interior domain measurement data. The article also provides numerical simulations, showing how to handle noisy data and reconstruct the parameters of the equation through Tikhonov regularization.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.