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

RESUMO

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 $f_1(x)g_1(t)\dot{B}^H(t)+f_2(x)g_2(t)$. 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.