Abstract

For a first-order hyperbolic system of integro-differential equations with a convolution-type integral term, we study the inverse problem of determining the convolution kernel. The direct problem is an initial–boundary value problem for this system on a finite interval \([0, H] \). Under some data consistency conditions, the inverse problem is reduced to a system of Volterra type integral equations. Further, the contraction mapping principle is applied to this system, and a theorem on the unique local solvability of the problem is proved for sufficiently small \(H\).

中文翻译：

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具有记忆的一阶双曲系统的反问题

摘要

对于具有卷积型积分项的积分微分方程的一阶双曲系统，我们研究了确定卷积核的反问题。对于系统，直接问题是在有限区间\（[0，H] \）上的初边值问题 。在某些数据一致性条件下，反问题简化为Volterra型积分方程组。此外，将压缩映射原理应用于该系统，并且证明了对于足够小的\（H \），该问题的唯一局部可解性的一个定理。