A Truncated-Kernel Mollification Method for the Cauchy Problem of the Modified Helmholtz Equation

This paper addresses the Cauchy problem for the multi-dimensional modified Helmholtz equation, a classical and severely ill-posed problem. A truncated-kernel mollification method is proposed as an effective regularization approach. Both the a priori and a posteriori regularization parameter choice strategies are examined, and the associated error estimates and convergence rates of the regularized solutions are established. The practical viability and effectiveness of the method are further validated through numerical experiments.