The paper aims to extend the notion of regional observability with constraints on the gradient (also called regional enlarged observability) to the semilinear parabolic case, in order to reconstruct the gradient of the initial data between two prescribed functions in an internal subregion $\omega$ of the evolution domain $\Omega$. The approach is based on an extension of the Hilbert Uniqueness Method (HUM) combined with the fixed point techniques. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations.

中文翻译：

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基于HUM方法的梯度约束半线性抛物型系统的可观测性。

本文旨在将对梯度具有约束力的区域可观测性概念（也称为区域扩大的可观测性）扩展到半线性抛物线情形，以重建内部子区域中两个指定函数之间的初始数据的梯度 $\omega$ 进化域 $\Omega$。该方法基于希尔伯特唯一性方法（HUM）与定点技术相结合的扩展。通过分析得出了一种算法，该算法已成功实现了数字化，并通过示例和仿真进行了说明。