Quasireversibility for a Nonlinear Nonlocal Parabolic Inverse Source Problem With Robin Boundary Conditions

Ngo Ngoc Hung

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-13

Abstract: We investigate an inverse source problem for a nonlinear parabolic equation with a nonlocal diffusion coefficient under Robin boundary conditions. The unknown source has the separated form, where p is known, and the spatial component g is recovered from final-time data. Compared to the Neumann case, the Robin condition changes the spectral structure of the associated elliptic operator and requires a regularization analysis based on the Robin Laplacian. We first establish a spectral representation of the weak solution. Then, we construct an improved quasireversibility method by introducing a frequency-dependent regularizing filter. Under suitable admissibility and fixed-point assumptions, we prove the existence of regularized solutions and derive a logarithmic convergence rate for noisy final-time data.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:9329805

DOI: 10.1155/ijmm/9329805

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