Rescaled kernel regularization for a nonlinear inverse problem with a sum of nonlocal diffusion operators

SDG4-Giáo dục có chất lượng
SDG9-Công nghệ - sáng tạo và phát triển hạ tầng

Abstract

This article tackles the ill-posed challenge of solving a nonlinear heat transfer equation in backward form. Traditional regularization methods (Tikhonov, quasi-reversibility, quasi-boundary value, truncation, etc.) exist, but we introduce a novel approach based on nonlocal diffusion equations with a rescaled convolution kernel. We will provide error estimates and demonstrate the accuracy of this technique under specific assumptions.

Nguyen, D.M., Dang, D.T. and Bui, T.D. (2026) Communications in Nonlinear Science and Numerical Simulation, 152(Part C), p. 109258.

DOI: https://doi.org/10.1016/j.cnsns.2025.109258