An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation (Q6546900)

The article discusses an inverse source problem (ISP) for a multidimensional, semilinear, backward parabolic equation, focusing on the existence and uniqueness of solutions. The authors employ the contraction principle and the Banach fixed-point theorem to establish unique solvability under specific conditions. They propose an iterative difference scheme for the numerical solution, demonstrating that this scheme also has unique solvability. The findings are significant for applications in various fields, including heat conduction and diffusion processes, particularly given the challenges posed by nonlinearities in ISPs.\N\NIn addition to theoretical results, the authors conduct numerical tests on two model problems, providing a comprehensive error analysis and visualizations to validate their method's effectiveness. The iterative scheme shows promising performance as long as the problem functions maintain a contractivity factor less than one. The study concludes with suggestions for future work, particularly regarding the handling of noisy data scenarios, thereby contributing valuable insights to the literature on nonlinear ISPs and their numerical solutions.