Inverse source problem for recovering a space-dependent factor in a Caputo–Hadamard pseudo-parabolic equation
Year: 2026
Type: article
Abstract: We study a terminal inverse source problem for a pseudo-parabolic equation with the Caputo–Hadamard fractional derivative, where a space-dependent factor in f ( x ) q ( t ) {f(x)q(t)} is recovered from final data. By spectral decomposition of the Dirichlet Laplacian, we derive an explicit solution formula and characterize the forward operator. The forward coefficients satisfy H n ≍ λ n - 1 {H_{n}\asymp\lambda_{n}^{-1}} , yielding a two-order spatial smoothing effect. Under a positivity condition on q , we prove uniqueness, a Picard-type range characterization, well-posedness in ℋ 2 ( Ω ) {\mathcal{H}^{2}(\Omega)} , ill-posedness in L 2 ( Ω ) {L^{2}(\Omega)} , and a conditional stability estimate. For noisy data, we analyze Tikhonov regularization and Landweber iteration under a priori and Morozov-type a posteriori parameter choices, and establish convergence and Hölder-type error estimates under standard source conditions. Numerical experiments illustrate the theory and compare the two reconstruction methods.
Author: Nguyen Hoang Luc
Institution: Ho Chi Minh University of Banking
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7171532660