由分数布朗运动驱动的Moore-Gibson-Thompson方程的逆随机源问题
An Inverse Random Source Problem for the Moore-Gibson-Thompson Equation Driven by Fractional Brownian Motion
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中文总结 AI 辅助
本文研究分数布朗运动驱动的随机Moore-Gibson-Thompson方程的逆随机源问题，证明了温和解的存在唯一性，并利用边界通量唯一恢复源项中的空间或时间函数。
中文摘要 AI 辅助
本文考虑由Hurst指数$H \in (0, 1)$的分数布朗运动驱动的随机Moore-Gibson-Thompson方程的逆随机源问题，其形式为$f_1(x)g_1(t)\dot{B}^H(t)+f_2(x)g_2(t)$。给定随机源，我们验证了温和解的存在性和唯一性。对于逆问题，我们证明了当$H \in(0,1)$时，若时间函数$g_i$已知，则可以从特殊非空开子集上的边界通量唯一恢复强度$f_i(x)$；若空间函数$f_i$已知，则可以唯一恢复$g_i(t)$。
英文摘要
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.
