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.

