In this work, two-dimensional inverse quasi-linear parabolic problem with periodic boundary and integral overdetermination conditions is investigated. The formal solution is obtained by the Fourier approximation. Under some natural regularity and consistency conditions on the input data,the existence, uniqueness and continuously dependence upon the data of the solution are proved by iteration method. The inverse problem is first examined by linearization and then used implicit finite difference scheme for the numerical solution. Also predictor corrector method is considered in the numerical approach. Some results on the numerical solution with two examples are presented with figures and tables. The sensitivity of the scheme with respect to noisy overdetermination data is illustrated.

在这项工作中，研究了具有周期性边界和积分超定条件的二维逆拟线性抛物线问题。形式解是通过傅立叶近似获得的。在输入数据具有一定的自然规律性和一致性条件下，通过迭代法证明解的存在性、唯一性和对数据的持续依赖。逆问题首先通过线性化检查，然后使用隐式有限差分格式进行数值解。在数值方法中也考虑了预测校正方法。用图和表给出了两个例子的数值解的一些结果。说明了该方案对噪声超定数据的敏感性。