Theoretical analysis demonstrates stable source reconstruction in fractional diffusion systems via generalized quasi-reversibility, highlighting a robust framework for random inverse problems.
In this paper, we study an inverse random source problem for the fourth-order fractional diffusion equation, where the source is driven by fractional Brownian motion (fBm). For the direct problem, we establish regularity results for the solutions under specific conditions. For the inverse problem, we prove the uniqueness and instability of the reconstructed source term. To address the instability, a generalized quasi-reversibility method (GQRM) is introduced, and convergence estimates for the reconstruction errors are derived under a priori and a posteriori parameter selection rules. Finally, numerical examples are presented to validate the effectiveness of the regularization approach.
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Bei et al. (2026) studied this question.
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