In this study, we investigate an inverse source problem for the bi-parabolic equation. The problem is severely non-well-posed in the sense of Hadamard. A problem is called well-posed if it satisfies three conditions: existence, uniqueness, and stability of the solution. If any of these conditions fail, the problem becomes ill-posed. Based on our research experience, the stability properties of the sought solution are often violated, hence necessitating a regularization method.

Here, we apply a Modified Quasi Boundary Method to handle the inverse source problem. Using this approach, we derive a regularized solution and demonstrate that it satisfies the well-posedness conditions in the sense of Hadamard. Furthermore, we provide an estimation of the convergence between the regularized solution and the exact solution by employing an a priori regularization parameter choice rule.