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arXiv · 2106.00917

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

Daxin Nie·Weihua Deng
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Abstract

We study the inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion with Hurst index $H\in(0,1)$. 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 the sign. Next, combining the properties of Mittag-Leffler function, the complete uniqueness and instability analyses are provided. It's worth mentioning that all the analyses are unified for $H\in(0,1)$.

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Daxin Nie, Weihua Deng. 2021-06-02. An inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion. https://arxiv.org/abs/2106.00917

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