An Inverse Random Source Problem for the Moore-Gibson-Thompson Equation Driven by Fractional Brownian Motion

Lingxi Gao; Yeqiong Ye; Ting Zhou

paper

An Inverse Random Source Problem for the Moore-Gibson-Thompson Equation Driven by Fractional Brownian Motion

arXiv:2609.08643

Abstract

In this paper, we consider an inverse random source problem for the stochastic Moore-Gibson-Thompson equation driven by fractional Brownian motion with Hurst index $H \in (0, 1)$ of the form $f_{1} (x) g_{1} (t) B ˙^{H} (t) + f_{2} (x) g_{2} (t)$ . Given the random source, existence and uniqueness of mild solutions are verified. For the inverse problem, the uniqueness of recovering the strength $f_{i} (x)$ if the time functions $g_{i}$ are known and $g_{i} (t)$ if the spatial functions $f_{i}$ are known when $H \in (0, 1)$ from the boundary flux on a special nonempty open subset is proved.