Solving two kinds of inverse source problems for the heat equations by a mollification regularization method with Dirichlet kernel

We study the inverse issues for the heat equations with spatial‐dependent source and time‐dependent source, respectively. In this work, the source identification issues are ill‐posed, and the numerical solutions (if they exist) are not continuously dependent on the data. A mollification regularization method with Dirichlet kernel is proposed to tackle the presented problems. Convergence analyses are carried out via two regularization parameter selection rules (a priori and a posteriori), respectively. Ultimately, a series of numerical experiments are presented to verify our theoretical results.