In this paper, we consider the final boundary value problem for non-local Kirchhoff’s model of parabolic type with discrete random noise. We first discuss the instability of solutions. Then we present the regularized solution by the trigonometric method in non-parametric regression associated with the truncated expansion method. In addition, under a prior assumption on the exact solution, the convergence rate is obtained. In the last section, the effectiveness and suitability of our results are justified via numerical experiments.

中文翻译：

---

具有离散随机噪声的抛物线型基尔霍夫模型的后向问题的近似解

在本文中，我们考虑了具有离散随机噪声的抛物型非局部Kirchhoff模型的最终边值问题。我们首先讨论解决方案的不稳定性。然后我们提出了与截断展开法相关的非参数回归中的三角法正则化解。另外，在关于精确解的先前假设下，获得收敛速度。在最后一部分中，通过数值实验证明了我们的结果的有效性和适用性。