Theoretical analysis demonstrates the convergence of Fourier truncation regularization for noisy fractional bi-parabolic systems, indicating effective reconstruction methods.
Key Points
Develop and analyze a regularization strategy for the ill-posed backward problem of a nonlinear fractional bi-parabolic equation driven by Gaussian white noise and a locally Lipschitz source term.
Formulated the backward problem using the fractional Laplacian and perturbed input data containing Gaussian white noise.
Applied the Fourier truncation method to regularize the ill-posed inverse system and derived theoretical convergence rates.
Conducted numerical experiments to evaluate the accuracy and stability of the regularized solution.
Established the mathematical ill-posedness of the backward nonlinear fractional bi-parabolic system under noise perturbation.
Proved explicit convergence rates between the exact solution and the regularized solution obtained via Fourier truncation.
Demonstrated through numerical examples that the regularization method effectively stabilizes the reconstruction process.