We consider a reaction-diffusion model of biological invasion in which the evolution of the population is governed by several parameters among them the intrinsic growth rate $ \mu(x) $. The knowledge of this growth rate is essential to predict the evolution of the population, but it is a priori unknown for exotic invasive species. We prove uniqueness and unconditional Lipschitz stability for the corresponding inverse problem, taking advantage of the positivity of the solution inside the spatial domain and studying its behaviour near the boundary with maximum principles. Our results complement previous works by Cristofol and Roques [11,13].

中文翻译：

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非线性Fisher-KPP方程中增长率系数的Lipschitz稳定性

我们考虑生物扩散的反应扩散模型，其中种群的演化受几个参数控制，其中包括内在增长率$ \ mu（x）$。了解这一增长率对于预测种群的进化至关重要，但是对于外来入侵物种而言，这是先验未知的。我们利用空间域内部解的正性并以最大原理研究其在边界附近的行为，从而证明了相应反问题的唯一性和无条件Lipschitz稳定性。我们的结果补充了克里斯托弗尔和罗克斯[11，13]。