This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a time trace of their values at a fixed point on the boundary of the spatial domain. We show both uniqueness results and the convergence of an iteration scheme designed to recover these sources. This leads to a reconstructive method and we shall demonstrate its effectiveness by several illustrative examples.

中文翻译：

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重构反应扩散系统的逆问题

本文考虑了从由状态变量值在固定有限时间（普查类型数据）或其值的时间轨迹组成的叠加数据中恢复反应扩散系统中状态相关源项的逆问题空间域边界上的一个固定点。我们展示了唯一性结果和旨在恢复这些来源的迭代方案的收敛性。这导致了一种重构方法，我们将通过几个说明性示例来证明其有效性。