A stability estimate on the regularized solution of the backward heat equation

摘要

Inverse problems, where one looks for causes for observed or desired effects, are usually “ill-posed”, i.e., their solution is not unique or unstable with respect to data perturbations. We derive a stability estimate for the regularized solution of the backward heat equation which is needed for stable solution of this ill-posed problem. For this purpose, we construct a regularizer for a certain minimization problem and, in conclusion, the stability of this minimization procedure.