Abstract This paper deals with the problem of determining an unknown source and an unknown initial condition in a abstract final value parabolic problem. This problem is ill-posed in the sense that the solutions do not depend continuously on the data. To solve the considered problem a modified Tikhonov regularization method is proposed. Using this method regularized solutions are constructed and under boundary conditions assumptions, convergence estimates between the exact solutions and their regularized approximations are obtained. Moreover numerical results are presented to illustrate the accuracy and efficiency of the proposed method.

中文翻译：

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一类反抛物线问题的改进Tikhonov正则化方法

摘要 本文研究在抽象终值抛物线问题中确定未知源和未知初始条件的问题。这个问题是不适定的，因为解决方案并不持续依赖于数据。为了解决所考虑的问题，提出了一种改进的 Tikhonov 正则化方法。使用这种方法构建正则化解，并在边界条件假设下，获得精确解与其正则化近似值之间的收敛估计。此外，还给出了数值结果来说明所提出方法的准确性和效率。