UDC 517.9 We investigate the solution of the inverse problem for a linear two-dimensional parabolic equation with periodic boundary and integral overdetermination conditions.Under certain natural regularity and consistency conditions imposed on the input data, we establish the existence, uniqueness of the solution and its continuous dependence on the data by using the generalized Fourier method. In addition, an iterative algorithm is constructed for the numerical solution of this problem.

中文翻译：

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具有周期性边界条件的热传导边界值问题的求解

UDC 517.9 我们研究了具有周期性边界和积分超定条件的线性二维抛物线方程的反问题的解。在对输入数据施加一定的自然规律和一致性条件下，我们建立了解的存在性、唯一性及其使用广义傅立叶方法对数据进行连续依赖。此外，还针对该问题的数值求解构造了迭代算法。