Regularization of Nonhomogeneous Ill‐Posed Parabolic Cauchy Problems via a Two‐Parameter Method With Stability Estimates

This study aims to propose a regularization method for an ill‐posed Cauchy problem involving an unbounded linear operator in a Hilbert space, in order to obtain a stable approximate solution together with error estimates. The main idea of the method developed in this study is to simultaneously perturb both the right‐hand side of the equation f ( t ) and the final data g . Finally, a numerical example demonstrates the effectiveness of the proposed method.