Startseite An inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion
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An inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion

  • Daxin Nie und Weihua Deng ORCID logo EMAIL logo
Veröffentlicht/Copyright: 28. Februar 2023

Abstract

We study the inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion with Hurst index H ( 0 , 1 ) . With the aid of a novel estimate, by using the operator approach we propose regularity analyses for the direct problem. Then we provide a reconstruction scheme for the source terms f and g up to sign. Next, combining the properties of Mittag-Leffler function, the complete uniqueness and instability analyses are provided. It is worth mentioning that all the analyses are unified for H ( 0 , 1 ) .

MSC 2010: 35R60; 35R30

Award Identifier / Grant number: 12071195

Award Identifier / Grant number: 12201270

Award Identifier / Grant number: 12225107

Award Identifier / Grant number: 22JR5RA391

Award Identifier / Grant number: 2021CXZX-010

Award Identifier / Grant number: 2022M721439

Funding statement: This work was supported by the National Natural Science Foundation of China under Grant Nos. 12071195, 12201270, and 12225107, the Innovative Groups of Basic Research in Gansu Province under Grant No. 22JR5RA391, the Outstanding Graduates Student Project of Gansu Education Department under Grant No. 2021CXZX-010, and China Postdoctoral Science Foundation under Grant No. 2022M721439.

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Received: 2021-09-15
Revised: 2022-11-01
Accepted: 2023-01-23
Published Online: 2023-02-28
Published in Print: 2023-10-01

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