New type of the unique continuation property for a fractional diffusion equation and an inverse source problem

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-01-23 DOI:10.1186/s13661-024-01827-5

Wenyi Liu, Chengbin Du, Zhiyuan Li

引用次数: 0

Abstract

In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determination of spatially dependent source terms and fractional order from sparse boundary observation data is established.

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分式扩散方程和反源问题的新型唯一延续特性

本文研究了时间分数扩散方程的一种新型唯一延续性质。证明主要基于拉普拉斯变换和贝塞尔函数的性质。在应用中，建立了从稀疏边界观测数据同时确定空间依赖源项和分数阶的逆问题的唯一性。

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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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.