In the work we investigate the numerical solution to a class of inverse problems with respect to the system of differential equations of hyperbolic type. The specialties of considered problems are: 1) the impulse impacts are present in the system and it is necessary to determine the capacities and the place of their location; 2) the differential equations of the system are only related to boundary values, and arbitrarily; 3) because of the long duration of the object functioning, the exact values of the initial conditions are not known, but a set of possible values is given. The inverse problem under consideration is reduced to the problem of parametric optimal control without initial conditions with non-separated boundary conditions. For the solution it is proposed to use first-order optimization methods. The results of numerical experiments are given on the example of the inverse problem of fluid transportation in the pipeline networks of complex structure. The problem is to determine the locations and the volume of leakage of raw materials based on the results of additional observations of the state of the transportation process at internal points or at the ends of sections of the pipeline network.

中文翻译：

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确定双曲系统中源的位置和容量的反问题的数值解

在工作中，我们研究关于双曲型微分方程组的一类反问题的数值解。所考虑的问题的特殊性是：1）系统中存在冲动影响，有必要确定其能力和位置。2）系统的微分方程只与边界值有关，并且是任意的；3）由于对象运行的持续时间较长，因此尚不清楚初始条件的确切值，但给出了一组可能的值。所考虑的逆问题被简化为没有初始条件且边界条件不分离的参数最优控制问题。对于该解决方案，建议使用一阶优化方法。以复杂结构管网中流体输运反问题为例，给出了数值实验结果。问题是根据对管道网络内部点或区段末端的运输过程状态的其他观察结果，确定原材料泄漏的位置和泄漏量。