In this paper, we study a nonlinear inverse problem for a third-order partial differential equation with integral conditions. This inverse problem is formulated as an auxiliary inverse problem which, in turn, is reduced to the operator equation in a specified Banach space using the method of spectral analysis. Finally, the existence and uniqueness of this operator equation is proved by applying the contraction mapping principle.

中文翻译：

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具有积分条件的三阶偏微分方程的逆边值问题

在本文中，我们研究了带有积分条件的三阶偏微分方程的非线性逆问题。将该反问题表述为辅助反问题，然后使用频谱分析方法将其反解为指定Banach空间中的算子方程。最后，通过压缩映射原理证明了该算子方程的存在性和唯一性。