This study deals with the identification of source function from final time state observation in a two-dimensional hyperbolic problem. The solution to the direct problem is obtained by the weak solution approach and finite element method. In the part of the inverse problem, the trust-region method and Levenberg–Marquardt method, which are nonlinear least-squares optimization methods, are used for the identification of source function. The findings are presented with numerical examples.

中文翻译：

---

二维双曲问题中非线性优化的逆源识别

本研究涉及从二维双曲线问题中的最终时间状态观察中识别源函数。直接问题的解是通过弱解法和有限元法得到的。在反问题部分，采用了非线性最小二乘优化方法的信任域法和Levenberg-Marquardt法对源函数进行辨识。研究结果以数值例子呈现。