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

  • Lingxi Gao
  • Yeqiong Ye
  • Ting Zhou
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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 ∈ (0, 1) of the form f1(x)g1(t)ḂH(t)+f2(x)g2(t). Given the random source, existence and uniqueness of mild solutions are verified. For the inverse problem, the uniqueness of recovering the strength fi(x) if the time functions gi are known and gi(t) if the spatial functions fi are known when H ∈(0,1) from the boundary flux on a special nonempty open subset is proved.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026inverse,
  title = {{An Inverse Random Source Problem for the Moore-Gibson-Thompson Equation Driven by Fractional Brownian Motion}},
  author = {Lingxi Gao and Yeqiong Ye and Ting Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08643},
  eprint = {2609.08643},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08643},
}
RIS
TY  - UNPB
TI  - An Inverse Random Source Problem for the Moore-Gibson-Thompson Equation Driven by Fractional Brownian Motion
AU  - Lingxi Gao
AU  - Yeqiong Ye
AU  - Ting Zhou
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08643
UR  - https://arxiv.org/abs/2609.08643
AB  - 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 ∈ (0, 1) of the form f_1(x)g_1(t)Ḃ^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 ∈(0,1) from the boundary flux on a special nonempty open subset is proved.
ER  -